{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.52 * 8.314 * 483 / 60.2.\nFinal: {\"answer\": 301.5082, \"unit\": \"kPa\"}", "dedupe_signature": "a7c04e544ddfbb2e630b03852d9fada5f4bb27074b6bf4b6bb4696b925d207da", "difficulty": "medium", "final_answer": {"answer": 301.5082, "unit": "kPa"}, "id": "ideal_gas_000003_4.52_483_60.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.52 mol, T=483 K, and V=60.2 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 = 4.52 * 8.314 * 483 / 60.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.52, "temp_k": 483, "volume_l": 60.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 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 = 3.505 / 3.455.\nFinal: {\"answer\": 1.0145, \"unit\": \"mol/L\"}", "dedupe_signature": "daebe4c1da9972cf449caf9d947ef44236265d47c854e33ddad5d46ceba28d94", "difficulty": "medium", "final_answer": {"answer": 1.0145, "unit": "mol/L"}, "id": "molarity_000008_3.505_3455", "license": "Apache-2.0", "prompt": "A solution contains 3.505 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 = 3.505 / 3.455.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.505, "volume_ml": 3455}, "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)=18.12 and f(4.2)=21.96.\n3. The interval width is 0.8.\nFinal: {\"answer\": 16.032, \"unit\": \"area_units\"}", "dedupe_signature": "154cccfa92788429aa9a07c3b07fa9a6a986f721844936754f5e02b80dd16d21", "difficulty": "medium", "final_answer": {"answer": 16.032, "unit": "area_units"}, "id": "trapz_linear_000010_4.8_1.8_3.4_4.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+1.8 from x=3.4 to x=4.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.4)=18.12 and f(4.2)=21.96.\nThe interval width is 0.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 1.8, "slope": 4.8, "x0": 3.4, "x1": 4.2}, "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=277 degrees and keep the unit as newtons.\nFinal: {\"answer\": [6.6419, -54.0938], \"unit\": \"N\"}", "dedupe_signature": "e5d3a7771ce3291e30fddc8267b3723bd1f625c07f75d58e9aae07ada268a4cc", "difficulty": "medium", "final_answer": {"answer": [6.6419, -54.0938], "unit": "N"}, "id": "vector_components_000013_54.5_277", "license": "Apache-2.0", "prompt": "A vector has magnitude 54.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 277, "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. Use Newton's second law F = m a.\n2. Substitute m = 21.5 kg and a = 2.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 48.375, \"unit\": \"N\"}", "dedupe_signature": "9a4391b85da49542d443b8785d567b6f5362cf33017238e12c9a3ada064f3d43", "difficulty": "easy", "final_answer": {"answer": 48.375, "unit": "N"}, "id": "force_000018_21.5_2.25", "license": "Apache-2.0", "prompt": "A cart has mass 21.5 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 = 21.5 kg and a = 2.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.25, "mass": 21.5}, "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 = 14.4^2 and multiply by 0.5 * 18.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1876.608, \"unit\": \"J\"}", "dedupe_signature": "5256be3a8dc74f9cd4dff13cc314bb58c86f262f463ee66d7d9ffa60be0beb22", "difficulty": "easy", "final_answer": {"answer": 1876.608, "unit": "J"}, "id": "ke_000019_18.1_14.4", "license": "Apache-2.0", "prompt": "A body of mass 18.1 kg moves at 14.4 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 = 14.4^2 and multiply by 0.5 * 18.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.1, "velocity": 14.4}, "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 = 4.3 * 8.314 * 450 / 53.5.\nFinal: {\"answer\": 300.7026, \"unit\": \"kPa\"}", "dedupe_signature": "2eee5a54fe7f90a0cbe41ff884202b4ad2e560937b275d5d7e2f9a32dcfa83e5", "difficulty": "medium", "final_answer": {"answer": 300.7026, "unit": "kPa"}, "id": "ideal_gas_000021_4.3_450_53.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.3 mol, T=450 K, and V=53.5 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 = 4.3 * 8.314 * 450 / 53.5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.3, "temp_k": 450, "volume_l": 53.5}, "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 = 380 * 2.065 * 78.\nFinal: {\"answer\": 61206.6, \"unit\": \"J\"}", "dedupe_signature": "2745040ddb553b84538cc5ad25813b1c454e0b0a2b097c5a67a6cad6adfeb1a4", "difficulty": "easy", "final_answer": {"answer": 61206.6, "unit": "J"}, "id": "heat_q_000022_380_2.065_78", "license": "Apache-2.0", "prompt": "A 380 g sample has specific heat 2.065 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 = 380 * 2.065 * 78.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 78, "heat_capacity": 2.065, "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=112 V and R=147.9 ohm.\nFinal: {\"answer\": 84.8141, \"unit\": \"W\"}", "dedupe_signature": "9716dc88016e2113fdf30cca12d5413d539ec66e29b1cbf37aa1b70bee8f17de", "difficulty": "easy", "final_answer": {"answer": 84.8141, "unit": "W"}, "id": "ohm_power_000041_112_147.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 147.9 ohm and voltage 112 V across it. Compute the dissipated power 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 V and R=147.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 147.9, "voltage": 112.0}, "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) = -0.96 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\": -0.4004, \"unit\": \"state_units\"}", "dedupe_signature": "c5aa153161519ca1bd9b2842128f67132164459b9722da59462891e583c49372", "difficulty": "medium", "final_answer": {"answer": -0.4004, "unit": "state_units"}, "id": "euler_decay_000045_31.5_0.96_1.6_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.96 y with y(0)=31.5, 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) = -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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 31.5, "rate": 0.96, "step": 1.6, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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=60.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 350.6126, \"unit\": \"m\"}", "dedupe_signature": "02da22325475461436c3bec988332c61e32bfeeaa6c3430571e8032d41e69366", "difficulty": "medium", "final_answer": {"answer": 350.6126, "unit": "m"}, "id": "projectile_range_000056_60.5_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.5 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=60.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "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 = 2.95 * 8.314 * 295 / 64.0.\nFinal: {\"answer\": 113.0509, \"unit\": \"kPa\"}", "dedupe_signature": "635ded74b935120b664fcd8dfe1df67d8871995a94baf1495b6510c91265cf76", "difficulty": "medium", "final_answer": {"answer": 113.0509, "unit": "kPa"}, "id": "ideal_gas_000075_2.95_295_64.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.95 mol, T=295 K, and V=64.0 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 = 2.95 * 8.314 * 295 / 64.0.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.95, "temp_k": 295, "volume_l": 64.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.83, -0.355, -0.65], \"unit\": \"temperature_units\"}", "dedupe_signature": "c01688f7ac2164abbdb56150749bc768cd8086706a92353c9fc97ac266d8bafc", "difficulty": "hard", "final_answer": {"answer": [1.83, -0.355, -0.65], "unit": "temperature_units"}, "id": "heat_step_000083_0.1_-1.05_2.5_-0.65_-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=-1.05, right=0.95; current interior values are [2.5, -0.65, -0.85]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.5, -0.65, -0.85], "left": -1.05, "r": 0.1, "right": 0.95}, "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_000088(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_000088\"}", "dedupe_signature": "11f507e55c966203da354bc1b2e56438bb52aa2de9d99032df54900fb6dc873b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_000088"}, "id": "code_000088_unit_vector_000088", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_000088(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": "validation", "task_family": "python_code_generation", "variables": {"function": "unit_vector_000088"}, "verifier": {"function": "unit_vector_000088", "tests": ["ux, uy = unit_vector_000088(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_000088(0, 5) == (0, 1)", "try:\n    unit_vector_000088(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_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 * 3.865 * 90.\nFinal: {\"answer\": 349589.25, \"unit\": \"J\"}", "dedupe_signature": "2f6500b6d45dd94616d0350d84b5bd4279881709f5e8dee3f0fbdf141b7925b1", "difficulty": "easy", "final_answer": {"answer": 349589.25, "unit": "J"}, "id": "heat_q_000094_1005_3.865_90", "license": "Apache-2.0", "prompt": "A 1005 g sample has specific heat 3.865 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 = 1005 * 3.865 * 90.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 90, "heat_capacity": 3.865, "mass_g": 1005}, "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 = 4.84 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 871.955, \"unit\": \"g\"}", "dedupe_signature": "806b9e4d2f235f95f63a493962a6bba998b242b0518f3f1fd08c5913210d328d", "difficulty": "medium", "final_answer": {"answer": 871.955, "unit": "g"}, "id": "stoich_mass_000097_glucose_4.84", "license": "Apache-2.0", "prompt": "A sample contains 4.84 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 = 4.84 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.84}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "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=65.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 233.8797, \"unit\": \"m\"}", "dedupe_signature": "3df225529e6347c9daba3f085eafe77e0bd2279f8edc8d5c1cde2d69b120b0e6", "difficulty": "medium", "final_answer": {"answer": 233.8797, "unit": "m"}, "id": "projectile_range_000110_65.8_74", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 65.8 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=65.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 74, "gravity": 9.81, "speed": 65.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_000124(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_000124\"}", "dedupe_signature": "3f95766dab56774e642f9721051dec056ed4abd4a3193511f9e3eb9558e8eb0b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000124"}, "id": "code_000124_safe_mean_000124", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000124(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": "validation", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000124"}, "verifier": {"function": "safe_mean_000124", "tests": ["assert safe_mean_000124([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000124(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000124([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_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\": [95.2722, -46.4673], \"unit\": \"N\"}", "dedupe_signature": "4d4fbf0b9a006178c1a7d960820338d5f1dac84c14832c70bade20b872ba439b", "difficulty": "medium", "final_answer": {"answer": [95.2722, -46.4673], "unit": "N"}, "id": "vector_components_000139_106_334", "license": "Apache-2.0", "prompt": "A vector has magnitude 106 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 334, "magnitude": 106.0}, "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. 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=50.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 229.9676, \"unit\": \"m\"}", "dedupe_signature": "8b6c55fae4c9d3bae05748bbc6cba07f4d816e16ca00c689eeb3f4c01f770414", "difficulty": "medium", "final_answer": {"answer": 229.9676, "unit": "m"}, "id": "projectile_range_000146_50.1_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.1 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=50.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2820 mL to 2.82 L.\n3. Compute M = 1.2 / 2.82.\nFinal: {\"answer\": 0.4255, \"unit\": \"mol/L\"}", "dedupe_signature": "e7c95fc7ff6d14bcf799af99ac6e12944d6864cdc87ac95b78bc7e4a3c8c05ee", "difficulty": "medium", "final_answer": {"answer": 0.4255, "unit": "mol/L"}, "id": "molarity_000152_1.2_2820", "license": "Apache-2.0", "prompt": "A solution contains 1.2 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 = 1.2 / 2.82.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 1.2, "volume_ml": 2820}, "verifier": {"formula": "moles / (volume_ml / 1000)", "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 89.5 + 273.15.\nFinal: {\"answer\": 362.65, \"unit\": \"K\"}", "dedupe_signature": "2d5772feba51b5592a1449122f10890344b84c01e9d74e72e5a79c2d34b5bf3d", "difficulty": "easy", "final_answer": {"answer": 362.65, "unit": "K"}, "id": "unit_convert_000156_c_to_k_89.5", "license": "Apache-2.0", "prompt": "Convert 89.5 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 89.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 89.5}, "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\": [-7.65, 23.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3bfa98fbcb1bc2f5fea945255e8dabacddf89e11a1db9d6fa62b493ebc4a611f", "difficulty": "medium", "final_answer": {"answer": [-7.65, 23.75], "unit": "dimensionless"}, "id": "line_two_point_000158_10.5_18.75_-7.65_23.75", "license": "Apache-2.0", "prompt": "A line passes through points (10.5, -56.575) and (18.75, -119.688). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 10.5, "x2": 18.75, "y1": -56.575, "y2": -119.6875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.6 kg and a = 6.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 162.84, \"unit\": \"N\"}", "dedupe_signature": "04fbee4035b1fe4a5a287cc6a0bf946256521d83e3fc0d0b1e2b3685819d3aa4", "difficulty": "easy", "final_answer": {"answer": 162.84, "unit": "N"}, "id": "force_000162_23.6_6.9", "license": "Apache-2.0", "prompt": "A cart has mass 23.6 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 = 23.6 kg and a = 6.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.9, "mass": 23.6}, "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 = 11.6^2 and multiply by 0.5 * 24.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1658.452, \"unit\": \"J\"}", "dedupe_signature": "11c05e7b031c166068c6e736c8908dc968234f75ce341a59877834837c72df66", "difficulty": "easy", "final_answer": {"answer": 1658.452, "unit": "J"}, "id": "ke_000163_24.65_11.6", "license": "Apache-2.0", "prompt": "A body of mass 24.65 kg moves at 11.6 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 = 11.6^2 and multiply by 0.5 * 24.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.65, "velocity": 11.6}, "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 = 1900 * 2.595 * 106.\nFinal: {\"answer\": 522633.0, \"unit\": \"J\"}", "dedupe_signature": "307395d5c80c8b7142413cca2ab7afbaf9fce4c31350b2effdad98a675811961", "difficulty": "easy", "final_answer": {"answer": 522633.0, "unit": "J"}, "id": "heat_q_000166_1900_2.595_106", "license": "Apache-2.0", "prompt": "A 1900 g sample has specific heat 2.595 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 = 1900 * 2.595 * 106.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 106, "heat_capacity": 2.595, "mass_g": 1900}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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_000196(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_000196\"}", "dedupe_signature": "a4ae6d2bde32de4955e9e90fd0717207aabee58452133e17c6bc3a962ec5921a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_000196"}, "id": "code_000196_center_values_000196", "license": "Apache-2.0", "prompt": "Write a Python function center_values_000196(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": "validation", "task_family": "python_code_generation", "variables": {"function": "center_values_000196"}, "verifier": {"function": "center_values_000196", "tests": ["out = center_values_000196([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_000196([5]) == [0]", "try:\n    center_values_000196([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.55, 22.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "4dff4bce4c16ec44d5630057271384065fce2b20026f97302875c6df82653256", "difficulty": "medium", "final_answer": {"answer": [-4.55, 22.5], "unit": "dimensionless"}, "id": "line_two_point_000212_-12.5_-0.25_-4.55_22.5", "license": "Apache-2.0", "prompt": "A line passes through points (-12.5, 79.375) and (-0.25, 23.6375). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -12.5, "x2": -0.25, "y1": 79.375, "y2": 23.6375}, "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": "df2b78b974415628b3dc18281e28a79eac7cc8ae226cf5e48836318203b1aa86", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000213_consistent_03f5e041_508093", "license": "Apache-2.0", "prompt": "In field worksheet case 508093, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 10.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "0647b1fc789183630ccc0bd8892406ef23397719f2cfb6ca8966d5410f60918c", "difficulty": "medium", "final_answer": {"answer": [-4.6, 10.0], "unit": "dimensionless"}, "id": "line_two_point_000248_5.25_14.25_-4.6_10", "license": "Apache-2.0", "prompt": "A line passes through points (5.25, -14.15) and (14.25, -55.55). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 5.25, "x2": 14.25, "y1": -14.149999999999999, "y2": -55.55}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 970 * 4.345 * 21.\nFinal: {\"answer\": 88507.65, \"unit\": \"J\"}", "dedupe_signature": "25572dcd2bbe137d5c1a441a1fd5549c68b5bf04b5aefa615ab0e4e87645a694", "difficulty": "easy", "final_answer": {"answer": 88507.65, "unit": "J"}, "id": "heat_q_000256_970_4.345_21", "license": "Apache-2.0", "prompt": "A 970 g sample has specific heat 4.345 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 = 970 * 4.345 * 21.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 4.345, "mass_g": 970}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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": "c53a2aab91314402390d34632c3e1ff75ec18658c911b5c332c8f493e3f53b92", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000285_consistent_4153435f_721824", "license": "Apache-2.0", "prompt": "In instrument manual case 721824, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8.65^2 and multiply by 0.5 * 25.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 963.3397, \"unit\": \"J\"}", "dedupe_signature": "37df06deb5fa21d231088f23c4b6fd1a426b8c78839e388c5ec79ead37c8fad0", "difficulty": "easy", "final_answer": {"answer": 963.3397, "unit": "J"}, "id": "ke_000289_25.75_8.65", "license": "Apache-2.0", "prompt": "A body of mass 25.75 kg moves at 8.65 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 = 8.65^2 and multiply by 0.5 * 25.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.75, "velocity": 8.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.45 kg and a = 8.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 188.7725, \"unit\": \"N\"}", "dedupe_signature": "583649b592cf74575198abfe15a6a5ae52e8dc168fd5ecf13b1827a6244cc35b", "difficulty": "easy", "final_answer": {"answer": 188.7725, "unit": "N"}, "id": "force_000306_23.45_8.05", "license": "Apache-2.0", "prompt": "A cart has mass 23.45 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 = 23.45 kg and a = 8.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.05, "mass": 23.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"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\": 1.5671, \"unit\": \"state_units\"}", "dedupe_signature": "81e8683a89ea8d82d99b7354bad6afa4e40ad2e5711056f3371990e54027532b", "difficulty": "medium", "final_answer": {"answer": 1.5671, "unit": "state_units"}, "id": "euler_decay_000315_5_0.15_0.9_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=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) = -0.15 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 5.0, "rate": 0.15, "step": 0.9, "steps": 8}, "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 12346.0 / 1000.\nFinal: {\"answer\": 12.346, \"unit\": \"kg\"}", "dedupe_signature": "5f3dfee4f9a59885b08f65afde66b52e1c2d5f04f53c1c6be59a87dc2f0700f5", "difficulty": "easy", "final_answer": {"answer": 12.346, "unit": "kg"}, "id": "unit_convert_000318_g_to_kg_12346", "license": "Apache-2.0", "prompt": "Convert 12346 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 12346.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 12346.0}, "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": "86dc436e5acc0852536ddce09dbf4d1789abf674b510a399375a3ee20faa6b41", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000321_inconsistent_56040f5d_398689", "license": "Apache-2.0", "prompt": "In student derivation case 398689, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=91.9 V and R=192.8 ohm.\nFinal: {\"answer\": 43.805, \"unit\": \"W\"}", "dedupe_signature": "46880856a28d799b24e391459904d01e6595d48d942a41d6b859e7417db7109a", "difficulty": "easy", "final_answer": {"answer": 43.805, "unit": "W"}, "id": "ohm_power_000329_91.9_192.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 192.8 ohm and voltage 91.9 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=91.9 V and R=192.8 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 192.8, "voltage": 91.9}, "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(9.9)=28.82 and f(19.5)=74.9.\n3. The interval width is 9.6.\nFinal: {\"answer\": 497.856, \"unit\": \"area_units\"}", "dedupe_signature": "8db8d5850d42e146f42138594a95dbe07fc99b91be1a4b23506dfcade4e54863", "difficulty": "medium", "final_answer": {"answer": 497.856, "unit": "area_units"}, "id": "trapz_linear_000334_4.8_-18.7_9.9_19.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-18.7 from x=9.9 to x=19.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.9)=28.82 and f(19.5)=74.9.\nThe interval width is 9.6.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -18.7, "slope": 4.8, "x0": 9.9, "x1": 19.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1010 mL to 1.01 L.\n3. Compute M = 3.435 / 1.01.\nFinal: {\"answer\": 3.401, \"unit\": \"mol/L\"}", "dedupe_signature": "39d068a1ae866625bbb9c041fa3776d64a1fa20431e31240a12503f8e8927787", "difficulty": "medium", "final_answer": {"answer": 3.401, "unit": "mol/L"}, "id": "molarity_000350_3.435_1010", "license": "Apache-2.0", "prompt": "A solution contains 3.435 mol of solute in 1010 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1010 mL to 1.01 L.\nCompute M = 3.435 / 1.01.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.435, "volume_ml": 1010}, "verifier": {"formula": "moles / (volume_ml / 1000)", "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 4408.5 / 100.\nFinal: {\"answer\": 44.085, \"unit\": \"m\"}", "dedupe_signature": "fdcc356f6d8b4934a699393d9656f3ea60c791d73c7ce9131b918def25a447b5", "difficulty": "easy", "final_answer": {"answer": 44.085, "unit": "m"}, "id": "unit_convert_000354_cm_to_m_4408.5", "license": "Apache-2.0", "prompt": "Convert 4408.5 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 4408.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 4408.5}, "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": "b84e035ab717d2df9ecd24a6e3e497e7d577d1fd029fc696dda801e79e0ebaeb", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000375_inconsistent_7481c798_118439", "license": "Apache-2.0", "prompt": "In quality-control check case 118439, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.576, 0.07, -1.054], \"unit\": \"temperature_units\"}", "dedupe_signature": "2e15bed18de6d762f2af7f613c0ef417c98cda12359e2d97ad58bb8d9a687100", "difficulty": "hard", "final_answer": {"answer": [0.576, 0.07, -1.054], "unit": "temperature_units"}, "id": "heat_step_000389_0.24_-0.45_1.2_0.25_-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=-0.45, right=-1.5; current interior values are [1.2, 0.25, -1.45]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.2, 0.25, -1.45], "left": -0.45, "r": 0.24, "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 1303.0 / 1000.\nFinal: {\"answer\": 1.303, \"unit\": \"kg\"}", "dedupe_signature": "a84dabfd6cef8251d01b10a4424aed42eb2bff64660df72d22842aaa294b0645", "difficulty": "easy", "final_answer": {"answer": 1.303, "unit": "kg"}, "id": "unit_convert_000408_g_to_kg_1303", "license": "Apache-2.0", "prompt": "Convert 1303 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 1303.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 1303.0}, "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": "bd4675aaf6ae0443b4527cef2807ed98a3ba34d3f34a3786377d725d06b5a587", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000411_inconsistent_c1271127_343175", "license": "Apache-2.0", "prompt": "In lab notebook case 343175, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"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)=52.5 and f(-7)=44.8.\n3. The interval width is 1.4.\nFinal: {\"answer\": 68.11, \"unit\": \"area_units\"}", "dedupe_signature": "f4cf2b5ee04b92cfac4ee4c00bdd8768ee0eeb98f56bee920bdfb73329ed01c6", "difficulty": "medium", "final_answer": {"answer": 68.11, "unit": "area_units"}, "id": "trapz_linear_000424_-5.5_6.3_-8.4_-7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+6.3 from x=-8.4 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(-8.4)=52.5 and f(-7)=44.8.\nThe interval width is 1.4.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 6.3, "slope": -5.5, "x0": -8.4, "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. 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": "8f9aeebb317355c282167cfd230cc28794cc6707e672d631b0a69ae3fc50e8b8", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000429_consistent_5ca82cb9_940097", "license": "Apache-2.0", "prompt": "In quality-control check case 940097, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.7 kg and a = 1.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 0.875, \"unit\": \"N\"}", "dedupe_signature": "1aa07b000ff14c486a8cd201a20d8285ce10135ec80b0dc3e4bbb82753b62368", "difficulty": "easy", "final_answer": {"answer": 0.875, "unit": "N"}, "id": "force_000432_0.7_1.25", "license": "Apache-2.0", "prompt": "A cart has mass 0.7 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 = 0.7 kg and a = 1.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.25, "mass": 0.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=104 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-85.6404, 343.4847], \"unit\": \"N\"}", "dedupe_signature": "9461e9bed4fa69d9210f161fd662d461be1df0d42fe03e37ed45a1b643e75fdb", "difficulty": "medium", "final_answer": {"answer": [-85.6404, 343.4847], "unit": "N"}, "id": "vector_components_000445_354_104", "license": "Apache-2.0", "prompt": "A vector has magnitude 354 N at 104 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=104 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 104, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=281 mg, t=196 h, and T_half=80.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 51.9713, \"unit\": \"mg\"}", "dedupe_signature": "1c483e9db4b129f03d5245715b2ea03f5c37828062f063edb15fc6679e125822", "difficulty": "medium", "final_answer": {"answer": 51.9713, "unit": "mg"}, "id": "half_life_000474_281_80.5_196", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 281 mg. Its half-life is 80.5 hours. How many mg remain after 196 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=281 mg, t=196 h, and T_half=80.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 196.0, "half_life": 80.5, "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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.4)=-7.34 and f(12)=-34.7.\n3. The interval width is 7.6.\nFinal: {\"answer\": -159.752, \"unit\": \"area_units\"}", "dedupe_signature": "a4c922a42fb5786030e3ec5d06a75c99a0a60b66f7c258d0048b12ffe1bd8870", "difficulty": "medium", "final_answer": {"answer": -159.752, "unit": "area_units"}, "id": "trapz_linear_000496_-3.6_8.5_4.4_12", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+8.5 from x=4.4 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(4.4)=-7.34 and f(12)=-34.7.\nThe interval width is 7.6.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 8.5, "slope": -3.6, "x0": 4.4, "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. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24.15^2 and multiply by 0.5 * 17.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5176.0997, \"unit\": \"J\"}", "dedupe_signature": "3505deef0560f12ac19369b866c42a86dc35d660f45aecfae56b2864c6800d61", "difficulty": "easy", "final_answer": {"answer": 5176.0997, "unit": "J"}, "id": "ke_000505_17.75_24.15", "license": "Apache-2.0", "prompt": "A body of mass 17.75 kg moves at 24.15 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 = 24.15^2 and multiply by 0.5 * 17.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.75, "velocity": 24.15}, "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=370 mg, t=323.5 h, and T_half=101 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 40.1802, \"unit\": \"mg\"}", "dedupe_signature": "a00160da05e2f332cefccb44416d6f6bcf119e3b4d6bcc01c8b2b5529f5d5f6e", "difficulty": "medium", "final_answer": {"answer": 40.1802, "unit": "mg"}, "id": "half_life_000510_370_101_323.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 370 mg. Its half-life is 101 hours. How many mg remain after 323.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=370 mg, t=323.5 h, and T_half=101 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 323.5, "half_life": 101.0, "initial_amount": 370.0}, "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(1.1)=20.35 and f(8.8)=62.7.\n3. The interval width is 7.7.\nFinal: {\"answer\": 319.7425, \"unit\": \"area_units\"}", "dedupe_signature": "89dbc519c2835c1ac26b188b74dafb346b9623833fce0cf6f55164ad659eb7cc", "difficulty": "medium", "final_answer": {"answer": 319.7425, "unit": "area_units"}, "id": "trapz_linear_000514_5.5_14.3_1.1_8.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.5x+14.3 from x=1.1 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(1.1)=20.35 and f(8.8)=62.7.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 14.3, "slope": 5.5, "x0": 1.1, "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=0.32 and add it to the current value.\nFinal: {\"answer\": [1.784, 1.446, 1.334], \"unit\": \"temperature_units\"}", "dedupe_signature": "a0f83bc4e6f63288f28284a1fb3c9efa4448310a70d5d1c0dd628e9d710710a6", "difficulty": "hard", "final_answer": {"answer": [1.784, 1.446, 1.334], "unit": "temperature_units"}, "id": "heat_step_000515_0.32_2.5_2.6_0.15_1.75_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=2.5, right=2.05; current interior values are [2.6, 0.15, 1.75]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 0.15, 1.75], "left": 2.5, "r": 0.32, "right": 2.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.25 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 11.0025, \"unit\": \"g\"}", "dedupe_signature": "55c899be7528e7ef5cf11fe66f9a0209c9661d582df7fd7acc22a71b93510374", "difficulty": "medium", "final_answer": {"answer": 11.0025, "unit": "g"}, "id": "stoich_mass_000547_carbon_dioxide_0.25", "license": "Apache-2.0", "prompt": "A sample contains 0.25 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 = 0.25 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.25}, "verifier": {"formula": "moles * molar_mass", "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_000556(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_000556\"}", "dedupe_signature": "5622af2480430e0f4208e6c83d48393b39a962aea6c4d9d48ce6539d3ca147a5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_000556"}, "id": "code_000556_pairwise_ratios_000556", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_000556(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": "validation", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_000556"}, "verifier": {"function": "pairwise_ratios_000556", "tests": ["assert pairwise_ratios_000556([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_000556([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_000556([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.82 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 868.3519, \"unit\": \"g\"}", "dedupe_signature": "44dcf38ab2cd8eeee1b26eab1fa948605f28320993c565a25c40727426cd007b", "difficulty": "medium", "final_answer": {"answer": 868.3519, "unit": "g"}, "id": "stoich_mass_000565_glucose_4.82", "license": "Apache-2.0", "prompt": "A sample contains 4.82 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 = 4.82 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.82}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=296.5 mg, t=129 h, and T_half=109 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 130.5449, \"unit\": \"mg\"}", "dedupe_signature": "3bc00a5c10aceb70fbc9a2c048711b2ea2460a89eabdd2445822584362af4786", "difficulty": "medium", "final_answer": {"answer": 130.5449, "unit": "mg"}, "id": "half_life_000582_296.5_109_129", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 296.5 mg. Its half-life is 109 hours. How many mg remain after 129 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=296.5 mg, t=129 h, and T_half=109 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 129.0, "half_life": 109.0, "initial_amount": 296.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 140 * 2.135 * 43.\nFinal: {\"answer\": 12852.7, \"unit\": \"J\"}", "dedupe_signature": "9860561286e4b5983f54545fa1f60ef38050a7e6864aa9b8377280883d841c93", "difficulty": "easy", "final_answer": {"answer": 12852.7, "unit": "J"}, "id": "heat_q_000598_140_2.135_43", "license": "Apache-2.0", "prompt": "A 140 g sample has specific heat 2.135 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 = 140 * 2.135 * 43.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 43, "heat_capacity": 2.135, "mass_g": 140}, "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 = 1.35 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 135.1175, \"unit\": \"g\"}", "dedupe_signature": "9d83b59a6f9b309706917316d2ae7321cdf0a8ea151c95f637568d7d85fa15d2", "difficulty": "medium", "final_answer": {"answer": 135.1175, "unit": "g"}, "id": "stoich_mass_000601_calcium_carbonate_1.35", "license": "Apache-2.0", "prompt": "A sample contains 1.35 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 = 1.35 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.35}, "verifier": {"formula": "moles * molar_mass", "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_000610(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_000610\"}", "dedupe_signature": "7c4ce89d85c74f3ab92c9faeace6452d6419234a02a02a262989cda02ce6dade", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_000610"}, "id": "code_000610_clamp_000610", "license": "Apache-2.0", "prompt": "Write a Python function clamp_000610(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": "validation", "task_family": "python_code_generation", "variables": {"function": "clamp_000610"}, "verifier": {"function": "clamp_000610", "tests": ["assert clamp_000610(5, 0, 10) == 5", "assert clamp_000610(-2, 0, 10) == 0", "assert clamp_000610(12, 0, 10) == 10", "try:\n    clamp_000610(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"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 and f(4.1)=-4.79.\n3. The interval width is 8.1.\nFinal: {\"answer\": -42.0795, \"unit\": \"area_units\"}", "dedupe_signature": "762486904dab1e163fc675f8d5fbfe282e6712c447060c1647009cf6f7d6d68a", "difficulty": "medium", "final_answer": {"answer": -42.0795, "unit": "area_units"}, "id": "trapz_linear_000640_0.1_-5.2_-4_4.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.1x+-5.2 from x=-4 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)=-5.6 and f(4.1)=-4.79.\nThe interval width is 8.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -5.2, "slope": 0.1, "x0": -4.0, "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. 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 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "91a5ec0f1a893e97fa72c9acb5f1fa57cdd1b02300dbeaeda5c95e226a6326d4", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000657_70_0.73_1.35_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.73 y with y(0)=70, step size h=1.35, 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) = -0.73 y, so each step multiplies y by 1 - h*0.73.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 70.0, "rate": 0.73, "step": 1.35, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "fd1d7341e802478f6477c24a48cb6647bd06130b665d04c34da83e4192f9c7fe", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000675_79.5_0.62_1.95_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.62 y with y(0)=79.5, 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) = -0.62 y, so each step multiplies y by 1 - h*0.62.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 79.5, "rate": 0.62, "step": 1.95, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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=63.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 229.1243, \"unit\": \"m\"}", "dedupe_signature": "018b72bc622bb98d2b163a3b29647ae4d5b820beacfa9fbc7b476daa5161e4e7", "difficulty": "medium", "final_answer": {"answer": 229.1243, "unit": "m"}, "id": "projectile_range_000686_63.4_17", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 63.4 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=63.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 17, "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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.2)=30.06 and f(11.4)=38.42.\n3. The interval width is 2.2.\nFinal: {\"answer\": 75.328, \"unit\": \"area_units\"}", "dedupe_signature": "0b7253606ca6355521cb66b9922e01fad24debe0c9e6bf18d1a413bea48a820a", "difficulty": "medium", "final_answer": {"answer": 75.328, "unit": "area_units"}, "id": "trapz_linear_000694_3.8_-4.9_9.2_11.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+-4.9 from x=9.2 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(9.2)=30.06 and f(11.4)=38.42.\nThe interval width is 2.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -4.9, "slope": 3.8, "x0": 9.2, "x1": 11.399999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.6 kg and a = 15.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 291.09, \"unit\": \"N\"}", "dedupe_signature": "286efe01cc40071498302f225ad7cbcd0efe03c4f85e5f97f7028b8b9d6dd208", "difficulty": "easy", "final_answer": {"answer": 291.09, "unit": "N"}, "id": "force_000702_18.6_15.65", "license": "Apache-2.0", "prompt": "A cart has mass 18.6 kg and measured acceleration 15.65 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 = 18.6 kg and a = 15.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.65, "mass": 18.6}, "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=85.6 V and R=189.6 ohm.\nFinal: {\"answer\": 38.6464, \"unit\": \"W\"}", "dedupe_signature": "135fba1686e768e649780a9310887380fd52f5dad56764183b26e2d19bf393d6", "difficulty": "easy", "final_answer": {"answer": 38.6464, "unit": "W"}, "id": "ohm_power_000707_85.6_189.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 189.6 ohm and voltage 85.6 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=85.6 V and R=189.6 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 189.6, "voltage": 85.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "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=23.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 37.4278, \"unit\": \"m\"}", "dedupe_signature": "a9f1cd1371bce7cfd5c40818534c491f3181e2a0e5b5dcc3a06dd343f6c36dd2", "difficulty": "medium", "final_answer": {"answer": 37.4278, "unit": "m"}, "id": "projectile_range_000722_23.9_70", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 23.9 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=23.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 70, "gravity": 9.81, "speed": 23.9}, "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=100.1 V and R=80.3 ohm.\nFinal: {\"answer\": 124.7822, \"unit\": \"W\"}", "dedupe_signature": "0d84cb25428aece4a6f96f8aeb1f7450200c5dc9c41a7d749a9914d62901bd88", "difficulty": "easy", "final_answer": {"answer": 124.7822, "unit": "W"}, "id": "ohm_power_000743_100.1_80.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 80.3 ohm and voltage 100.1 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=100.1 V and R=80.3 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 80.3, "voltage": 100.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.54 * 8.314 * 440 / 48.0.\nFinal: {\"answer\": 41.1543, \"unit\": \"kPa\"}", "dedupe_signature": "1a3d40185e27056b7b5a8c7a6acfa84cd089b78242f00dacd51e65c7ef478dc0", "difficulty": "medium", "final_answer": {"answer": 41.1543, "unit": "kPa"}, "id": "ideal_gas_000759_0.54_440_48.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.54 mol, T=440 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 = 0.54 * 8.314 * 440 / 48.0.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.54, "temp_k": 440, "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. The function contract has a 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_000772(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_000772\"}", "dedupe_signature": "23a94feb23c16647b7e238afa8d9c030ee966403ddcff07d9f2e84fd9a6203fa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_000772"}, "id": "code_000772_center_values_000772", "license": "Apache-2.0", "prompt": "Write a Python function center_values_000772(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": "validation", "task_family": "python_code_generation", "variables": {"function": "center_values_000772"}, "verifier": {"function": "center_values_000772", "tests": ["out = center_values_000772([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_000772([5]) == [0]", "try:\n    center_values_000772([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=147.5 mg, t=106.5 h, and T_half=94 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 67.2561, \"unit\": \"mg\"}", "dedupe_signature": "f976d09cd2d40b3c939c19fb0ca0ef917e4c3f9906a279cb1e95c546d351f4d7", "difficulty": "medium", "final_answer": {"answer": 67.2561, "unit": "mg"}, "id": "half_life_000780_147.5_94_106.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 147.5 mg. Its half-life is 94 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=147.5 mg, t=106.5 h, and T_half=94 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 106.5, "half_life": 94.0, "initial_amount": 147.5}, "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 = 3.81 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 222.6564, \"unit\": \"g\"}", "dedupe_signature": "4bb391783d2bc32e4831b320dc9caa2dfd7bc7be32935eabb55beff22afd70f1", "difficulty": "medium", "final_answer": {"answer": 222.6564, "unit": "g"}, "id": "stoich_mass_000799_sodium_chloride_3.81", "license": "Apache-2.0", "prompt": "A sample contains 3.81 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 = 3.81 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.81}, "verifier": {"formula": "moles * molar_mass", "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 173.5 + 273.15.\nFinal: {\"answer\": 446.65, \"unit\": \"K\"}", "dedupe_signature": "5f4a150141bbd39315916f659365ae2c6a1aba3f91fce1f84f90f339bf5d4bc1", "difficulty": "easy", "final_answer": {"answer": 446.65, "unit": "K"}, "id": "unit_convert_000804_c_to_k_173.5", "license": "Apache-2.0", "prompt": "Convert 173.5 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 173.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 173.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1595 * 3.265 * 87.\nFinal: {\"answer\": 453067.725, \"unit\": \"J\"}", "dedupe_signature": "ad651288cb7f1a2191e9797df483d2ffc8c2e96c1dae0f9196a0abbe351d2c48", "difficulty": "easy", "final_answer": {"answer": 453067.725, "unit": "J"}, "id": "heat_q_000814_1595_3.265_87", "license": "Apache-2.0", "prompt": "A 1595 g sample has specific heat 3.265 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 = 1595 * 3.265 * 87.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 87, "heat_capacity": 3.265, "mass_g": 1595}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [208.2998, -181.0723], \"unit\": \"N\"}", "dedupe_signature": "4965da069e724dab6a5f643e40f2fbf4d5151c7cfa1607c552ca58bcccdde5c1", "difficulty": "medium", "final_answer": {"answer": [208.2998, -181.0723], "unit": "N"}, "id": "vector_components_000823_276_319", "license": "Apache-2.0", "prompt": "A vector has magnitude 276 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 319, "magnitude": 276.0}, "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": "b0a85f4d5337f202b9416a9ce4bc597b8ea6f05015b2471f564aea2e74c66dc1", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000825_consistent_03f5e041_467857", "license": "Apache-2.0", "prompt": "In instrument manual case 467857, 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": "validation", "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: 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": "1be7488d790a32c3ae5c18d18e831110689feb1800dffa98f55f18d0b7d6ade2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000827_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.2 and interior values [1.6, 2.35, -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": "validation", "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. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3624.5 / 100.\nFinal: {\"answer\": 36.245, \"unit\": \"m\"}", "dedupe_signature": "421eecf19c63797b8afadebf7ed8e2bc520427f17b34cde9df20e9c6b39c8168", "difficulty": "easy", "final_answer": {"answer": 36.245, "unit": "m"}, "id": "unit_convert_000840_cm_to_m_3624.5", "license": "Apache-2.0", "prompt": "Convert 3624.5 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 3624.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 3624.5}, "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. 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": "87baef0fb91016c4113746dac0dcfb4773556c262fd21f0738b16db2da2349c6", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000843_consistent_4153435f_972866", "license": "Apache-2.0", "prompt": "In field worksheet case 972866, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"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)=-23.22 and f(17.1)=-43.38.\n3. The interval width is 7.2.\nFinal: {\"answer\": -239.76, \"unit\": \"area_units\"}", "dedupe_signature": "b91de20b18f6d3667d94cdfb4d2a821f75a8fa0814492d454102af146cf2e5de", "difficulty": "medium", "final_answer": {"answer": -239.76, "unit": "area_units"}, "id": "trapz_linear_000856_-2.8_4.5_9.9_17.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+4.5 from x=9.9 to x=17.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.9)=-23.22 and f(17.1)=-43.38.\nThe interval width is 7.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 4.5, "slope": -2.8, "x0": 9.9, "x1": 17.1}, "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\": [1.132, 0.939, 1.306], \"unit\": \"temperature_units\"}", "dedupe_signature": "4f49a9ae3f8300ea1282667506ec305a899803acd53b8896bea422a847fc6b3a", "difficulty": "hard", "final_answer": {"answer": [1.132, 0.939, 1.306], "unit": "temperature_units"}, "id": "heat_step_000857_0.34_2.3_-0.5_1.5_1.85_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=2.3, right=0.6; current interior values are [-0.5, 1.5, 1.85]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.5, 1.5, 1.85], "left": 2.3, "r": 0.34, "right": 0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"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 * 22.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3135.2859, \"unit\": \"J\"}", "dedupe_signature": "2060fd4e3c73c7e6d009b6ffd4969f37ee95ec8589173908d60a54a4ffcd3c88", "difficulty": "easy", "final_answer": {"answer": 3135.2859, "unit": "J"}, "id": "ke_000883_22.35_16.75", "license": "Apache-2.0", "prompt": "A body of mass 22.35 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 * 22.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.35, "velocity": 16.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "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)=7.32 and f(-3.3)=10.89.\n3. The interval width is 5.1.\nFinal: {\"answer\": 46.4355, \"unit\": \"area_units\"}", "dedupe_signature": "cc2dc3107344fad32f339d2ede49718a8e9b7bc0af8358354371738d7bc6c39a", "difficulty": "medium", "final_answer": {"answer": 46.4355, "unit": "area_units"}, "id": "trapz_linear_000892_0.7_13.2_-8.4_-3.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+13.2 from x=-8.4 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(-8.4)=7.32 and f(-3.3)=10.89.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 13.2, "slope": 0.7, "x0": -8.4, "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 1028.5 / 100.\nFinal: {\"answer\": 10.285, \"unit\": \"m\"}", "dedupe_signature": "cb340d3785db5abb1cfb5f7c3859a6b8b40c90c043cf4806be41378e33941321", "difficulty": "easy", "final_answer": {"answer": 10.285, "unit": "m"}, "id": "unit_convert_000894_cm_to_m_1028.5", "license": "Apache-2.0", "prompt": "Convert 1028.5 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 1028.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 1028.5}, "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=22 degrees and keep the unit as newtons.\nFinal: {\"answer\": [295.7716, 119.4995], \"unit\": \"N\"}", "dedupe_signature": "9ab284b7c437d0e6a1020c89e348529daaaa889b3cc7d270915458a333704312", "difficulty": "medium", "final_answer": {"answer": [295.7716, 119.4995], "unit": "N"}, "id": "vector_components_000895_319_22", "license": "Apache-2.0", "prompt": "A vector has magnitude 319 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 22, "magnitude": 319.0}, "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\": [-9.65, -22.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0d274a127fd6e57be826e8da60805d7fa085c1318f43c11abb8404b0dd03d1f6", "difficulty": "medium", "final_answer": {"answer": [-9.65, -22.75], "unit": "dimensionless"}, "id": "line_two_point_000896_0.75_2.75_-9.65_-22.75", "license": "Apache-2.0", "prompt": "A line passes through points (0.75, -29.9875) and (2.75, -49.2875). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 0.75, "x2": 2.75, "y1": -29.9875, "y2": -49.2875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 14.2^2 and multiply by 0.5 * 23.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2409.598, \"unit\": \"J\"}", "dedupe_signature": "59f557d31f98b44fb621a8071cf10821bb264dcd856b30df101cbd4c2e80e25f", "difficulty": "easy", "final_answer": {"answer": 2409.598, "unit": "J"}, "id": "ke_000901_23.9_14.2", "license": "Apache-2.0", "prompt": "A body of mass 23.9 kg moves at 14.2 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 = 14.2^2 and multiply by 0.5 * 23.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.9, "velocity": 14.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "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 * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 457.3976, \"unit\": \"g\"}", "dedupe_signature": "7b53c2715627d6416a804fe879ddb64dc7659736b67f8f74941d2c0d08fb4260", "difficulty": "medium", "final_answer": {"answer": 457.3976, "unit": "g"}, "id": "stoich_mass_000907_calcium_carbonate_4.57", "license": "Apache-2.0", "prompt": "A sample contains 4.57 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 = 4.57 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "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 425 mL to 0.425 L.\n3. Compute M = 0.84 / 0.425.\nFinal: {\"answer\": 1.9765, \"unit\": \"mol/L\"}", "dedupe_signature": "4057866b84e0d8f6e7c343340a1a605957d93bc50783acde94f591652eb73b88", "difficulty": "medium", "final_answer": {"answer": 1.9765, "unit": "mol/L"}, "id": "molarity_000908_0.84_425", "license": "Apache-2.0", "prompt": "A solution contains 0.84 mol of solute in 425 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 425 mL to 0.425 L.\nCompute M = 0.84 / 0.425.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 0.84, "volume_ml": 425}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"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=14.5 h, and T_half=17 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 405.5522, \"unit\": \"mg\"}", "dedupe_signature": "dbacb815a9af0ab9a4c1b2deb89da63b254b11cf5e2e20e20ded9e63803acda6", "difficulty": "medium", "final_answer": {"answer": 405.5522, "unit": "mg"}, "id": "half_life_000924_732.5_17_14.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 732.5 mg. Its half-life is 17 hours. How many mg remain after 14.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=732.5 mg, t=14.5 h, and T_half=17 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 14.5, "half_life": 17.0, "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. 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": "b833eab5f9fe0a3e77ea41c2137355fca872d754544c952cb76d62ab1a0c5d20", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_000935_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 508 items and budget 51925, 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": "validation", "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. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=270 degrees and keep the unit as newtons.\nFinal: {\"answer\": [0.0, -171.0], \"unit\": \"N\"}", "dedupe_signature": "93b3d911f05e7c6971d9e601e9ccc1c94a8b07e9ca1434d465770281e3341bd1", "difficulty": "medium", "final_answer": {"answer": [0.0, -171.0], "unit": "N"}, "id": "vector_components_000949_171_270", "license": "Apache-2.0", "prompt": "A vector has magnitude 171 N at 270 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=270 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 270, "magnitude": 171.0}, "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. Use Newton's second law F = m a.\n2. Substitute m = 21.6 kg and a = 4.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 97.2, \"unit\": \"N\"}", "dedupe_signature": "1726c64350947ccda1d38f6a40afa4b4790d7aeb023ad02cbefb813299a8f74b", "difficulty": "easy", "final_answer": {"answer": 97.2, "unit": "N"}, "id": "force_000954_21.6_4.5", "license": "Apache-2.0", "prompt": "A cart has mass 21.6 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 = 21.6 kg and a = 4.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.5, "mass": 21.6}, "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=289.5 mg, t=51.5 h, and T_half=20.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 50.7461, \"unit\": \"mg\"}", "dedupe_signature": "b26f5f1db94a81e1a9d8924f0e9bffce02f655904478bb9acf0035c89d006ebe", "difficulty": "medium", "final_answer": {"answer": 50.7461, "unit": "mg"}, "id": "half_life_000960_289.5_20.5_51.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 289.5 mg. Its half-life is 20.5 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=289.5 mg, t=51.5 h, and T_half=20.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 51.5, "half_life": 20.5, "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. Mass equals amount in moles times molar mass.\n2. Use m = 8 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 467.52, \"unit\": \"g\"}", "dedupe_signature": "e675d38744fcc51480e18f1325ed79926bd3a235ea228b70b10b27bd294a61c6", "difficulty": "medium", "final_answer": {"answer": 467.52, "unit": "g"}, "id": "stoich_mass_000961_sodium_chloride_8", "license": "Apache-2.0", "prompt": "A sample contains 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 = 8 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 8.0}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=74 degrees and keep the unit as newtons.\nFinal: {\"answer\": [18.0542, 62.9626], \"unit\": \"N\"}", "dedupe_signature": "fc39fc74a6a4d756dc485a6bd9fcb8e7fa0f6c4e37e9840cd28d556f391da3b1", "difficulty": "medium", "final_answer": {"answer": [18.0542, 62.9626], "unit": "N"}, "id": "vector_components_000967_65.5_74", "license": "Apache-2.0", "prompt": "A vector has magnitude 65.5 N at 74 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=74 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 74, "magnitude": 65.5}, "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. Use Newton's second law F = m a.\n2. Substitute m = 13.65 kg and a = 8.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 113.295, \"unit\": \"N\"}", "dedupe_signature": "6848632874b04c2d064f773233c13e3468db9a6cdc2fcd06f3ba4ce46d665cac", "difficulty": "easy", "final_answer": {"answer": 113.295, "unit": "N"}, "id": "force_000972_13.65_8.3", "license": "Apache-2.0", "prompt": "A cart has mass 13.65 kg and measured acceleration 8.3 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 = 13.65 kg and a = 8.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.3, "mass": 13.65}, "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 = 2.81 * 8.314 * 561 / 30.0.\nFinal: {\"answer\": 436.8758, \"unit\": \"kPa\"}", "dedupe_signature": "79fb98f05309ab9d6134f28e84c841db6191d127ff94df85a0717f86dc7596d4", "difficulty": "medium", "final_answer": {"answer": 436.8758, "unit": "kPa"}, "id": "ideal_gas_000975_2.81_561_30.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.81 mol, T=561 K, and V=30.0 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 = 2.81 * 8.314 * 561 / 30.0.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.81, "temp_k": 561, "volume_l": 30.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.3^2 and multiply by 0.5 * 29.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 27607.7552, \"unit\": \"J\"}", "dedupe_signature": "4436a65724c3b7bf5e8f00891965ca63df6ac7835cf1738f0e05382a5c844e06", "difficulty": "easy", "final_answer": {"answer": 27607.7552, "unit": "J"}, "id": "ke_000991_29.45_43.3", "license": "Apache-2.0", "prompt": "A body of mass 29.45 kg moves at 43.3 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 = 43.3^2 and multiply by 0.5 * 29.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.45, "velocity": 43.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"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 7 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "f6b8d183a8beed4bda09f56a68c0852aa7e451def0de32e94b47307ed658b9fd", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000999_42_0.99_1.1_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.99 y with y(0)=42, 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) = -0.99 y, so each step multiplies y by 1 - h*0.99.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 42.0, "rate": 0.99, "step": 1.1, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.7 kg and a = 9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 168.3, \"unit\": \"N\"}", "dedupe_signature": "57cd46a895093ddcacea96f0f47fe241d0466a331afb7cf8ae442d05977c4b2c", "difficulty": "easy", "final_answer": {"answer": 168.3, "unit": "N"}, "id": "force_001008_18.7_9", "license": "Apache-2.0", "prompt": "A cart has mass 18.7 kg and measured acceleration 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 = 18.7 kg and a = 9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.0, "mass": 18.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.722, 1.488, 1.018], \"unit\": \"temperature_units\"}", "dedupe_signature": "de89edf620beebe3a5e9561e662835f0638039fa8be33054fa9da61b6ac6ba65", "difficulty": "hard", "final_answer": {"answer": [-0.722, 1.488, 1.018], "unit": "temperature_units"}, "id": "heat_step_001037_0.08_1.25_-1.15_1.8_0.85_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=1.25, right=2; current interior values are [-1.15, 1.8, 0.85]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-1.15, 1.8, 0.85], "left": 1.25, "r": 0.08, "right": 2.0}, "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\": [8.6, -14.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "6b4b97fc25b52de4989b22654dc2b8a880ec2b94aca2e51d0c17f4526e732162", "difficulty": "medium", "final_answer": {"answer": [8.6, -14.25], "unit": "dimensionless"}, "id": "line_two_point_001040_17.25_22_8.6_-14.25", "license": "Apache-2.0", "prompt": "A line passes through points (17.25, 134.1) and (22, 174.95). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 17.25, "x2": 22.0, "y1": 134.1, "y2": 174.95}, "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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.3)=-7.51 and f(-0.5)=-11.65.\n3. The interval width is 1.8.\nFinal: {\"answer\": -17.244, \"unit\": \"area_units\"}", "dedupe_signature": "1703e914703cd335b02771be03bbe4ed0b968350d4eef21dce1abe413106a0ce", "difficulty": "medium", "final_answer": {"answer": -17.244, "unit": "area_units"}, "id": "trapz_linear_001054_-2.3_-12.8_-2.3_-0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.3x+-12.8 from x=-2.3 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(-2.3)=-7.51 and f(-0.5)=-11.65.\nThe interval width is 1.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -12.8, "slope": -2.3, "x0": -2.3, "x1": -0.4999999999999998}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.302, 1.11, 1.026], \"unit\": \"temperature_units\"}", "dedupe_signature": "5acdf302bed34733a0f34eb31d352e6f8517290d2226e3db889799856e5bf05c", "difficulty": "hard", "final_answer": {"answer": [1.302, 1.11, 1.026], "unit": "temperature_units"}, "id": "heat_step_001055_0.32_1.35_0.15_2.55_0.45_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=1.35, right=0.15; current interior values are [0.15, 2.55, 0.45]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.15, 2.55, 0.45], "left": 1.35, "r": 0.32, "right": 0.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_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": "4475d05be3ca1c5c7695da820ddbb0aa809bbab027fd94c8691316dd8f29254f", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001079_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=10 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": "validation", "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 = 36.1^2 and multiply by 0.5 * 19.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12510.816, \"unit\": \"J\"}", "dedupe_signature": "2afda9fde994dc28f257cb10c215baf01dfc020d3c75c17c59e3f99f72c60679", "difficulty": "easy", "final_answer": {"answer": 12510.816, "unit": "J"}, "id": "ke_001081_19.2_36.1", "license": "Apache-2.0", "prompt": "A body of mass 19.2 kg moves at 36.1 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 = 36.1^2 and multiply by 0.5 * 19.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.2, "velocity": 36.1}, "verifier": {"formula": "0.5 * mass * velocity ** 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\": [3.4, 15.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "866b981b102cb653863c163899bc5c9821721263416bfb62e281f67708d6e9ca", "difficulty": "medium", "final_answer": {"answer": [3.4, 15.75], "unit": "dimensionless"}, "id": "line_two_point_001094_0.25_12.75_3.4_15.75", "license": "Apache-2.0", "prompt": "A line passes through points (0.25, 16.6) and (12.75, 59.1). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 0.25, "x2": 12.75, "y1": 16.6, "y2": 59.1}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=53.4 V and R=116.9 ohm.\nFinal: {\"answer\": 24.3932, \"unit\": \"W\"}", "dedupe_signature": "f3460f39a1959bbaa2f2713a25b0e3788e423ebf4915b58a4d11fe0cfa4ee635", "difficulty": "easy", "final_answer": {"answer": 24.3932, "unit": "W"}, "id": "ohm_power_001103_53.4_116.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 116.9 ohm and voltage 53.4 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=53.4 V and R=116.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 116.9, "voltage": 53.4}, "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=914 mg, t=21 h, and T_half=57 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 708.0117, \"unit\": \"mg\"}", "dedupe_signature": "1d7d803003c3bfb54c6130d99de5ab6f9e5faae4a4b168c138566076f43ae16a", "difficulty": "medium", "final_answer": {"answer": 708.0117, "unit": "mg"}, "id": "half_life_001104_914_57_21", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 914 mg. Its half-life is 57 hours. How many mg remain after 21 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=914 mg, t=21 h, and T_half=57 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 21.0, "half_life": 57.0, "initial_amount": 914.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "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": "67e25c69f9786229dc7e0b5eeaf0475a14ce7c8a1e010ff7a8cb767118ec7e70", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_001115_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 [1.35, 1.0, 2.55], 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": "validation", "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=11 degrees through the sine of 2 theta.\n3. Substitute v=13.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 6.9594, \"unit\": \"m\"}", "dedupe_signature": "9ce7985b99f2d42b34398c616041f14f06e34843b9fff8eb1d087607e7e0a24a", "difficulty": "medium", "final_answer": {"answer": 6.9594, "unit": "m"}, "id": "projectile_range_001118_13.5_11", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 13.5 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=13.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 11, "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. Mass equals amount in moles times molar mass.\n2. Use m = 5.7 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1026.8892, \"unit\": \"g\"}", "dedupe_signature": "c64f33bd91cd3f3bc7c6f503373b78558122370d1dc748c07b455994bb0c0885", "difficulty": "medium", "final_answer": {"answer": 1026.8892, "unit": "g"}, "id": "stoich_mass_001123_glucose_5.7", "license": "Apache-2.0", "prompt": "A sample contains 5.7 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 = 5.7 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.7}, "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(4.9)=30.93 and f(9.9)=54.43.\n3. The interval width is 5.\nFinal: {\"answer\": 213.4, \"unit\": \"area_units\"}", "dedupe_signature": "d0ada1b939cbf293ce5aa06e19771d5b0d19db48fb28624664e334b0e5d18a10", "difficulty": "medium", "final_answer": {"answer": 213.4, "unit": "area_units"}, "id": "trapz_linear_001126_4.7_7.9_4.9_9.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+7.9 from x=4.9 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(4.9)=30.93 and f(9.9)=54.43.\nThe interval width is 5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 7.9, "slope": 4.7, "x0": 4.9, "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=0.1 and add it to the current value.\nFinal: {\"answer\": [0.33, 0.095, -1.035], \"unit\": \"temperature_units\"}", "dedupe_signature": "e610d5c05d3c805e6d7993b52a8893ab76bf3c80067cd03724c0da98d6ad0f12", "difficulty": "hard", "final_answer": {"answer": [0.33, 0.095, -1.035], "unit": "temperature_units"}, "id": "heat_step_001127_0.1_1.45_0.2_0.25_-1.25_-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 [0.2, 0.25, -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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.2, 0.25, -1.25], "left": 1.45, "r": 0.1, "right": -0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=214.4 V and R=80.4 ohm.\nFinal: {\"answer\": 571.7333, \"unit\": \"W\"}", "dedupe_signature": "19301dc33a7ff80fcf463aa24fa3d3bdddfcabb00578dbd8f0a87e5775d69afb", "difficulty": "easy", "final_answer": {"answer": 571.7333, "unit": "W"}, "id": "ohm_power_001139_214.4_80.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 80.4 ohm and voltage 214.4 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=214.4 V and R=80.4 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 80.4, "voltage": 214.4}, "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) = -0.09 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\": 15.6094, \"unit\": \"state_units\"}", "dedupe_signature": "ca385e7158d3e3ffcbb6e0df6ff86e0cbac680283debce7d2a883a096addff8d", "difficulty": "medium", "final_answer": {"answer": 15.6094, "unit": "state_units"}, "id": "euler_decay_001143_44_0.09_1.35_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=44, step size h=1.35, 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) = -0.09 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 44.0, "rate": 0.09, "step": 1.35, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=94.1 V and R=66.2 ohm.\nFinal: {\"answer\": 133.7585, \"unit\": \"W\"}", "dedupe_signature": "e4bb785287dadb5888ca2a309b151b3e1803d9e2ba4221a7c72d2246b080f6ff", "difficulty": "easy", "final_answer": {"answer": 133.7585, "unit": "W"}, "id": "ohm_power_001157_94.1_66.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 66.2 ohm and voltage 94.1 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=94.1 V and R=66.2 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 66.2, "voltage": 94.1}, "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) = -0.76 y, so each step multiplies y by 1 - h*0.76.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "336a47dbeee736380fa497a2197c8180b37ee57eedb7d290e2eaa06a987075d1", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_001161_29.5_0.76_0.95_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.76 y with y(0)=29.5, step size h=0.95, 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) = -0.76 y, so each step multiplies y by 1 - h*0.76.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 29.5, "rate": 0.76, "step": 0.95, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_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": "296b3b0536e1c1f2637b351084fe230f5dda6d2b5a39f25f0ef4544f02884fc0", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001169_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field crop record from batch 292762 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": "validation", "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. Mass equals amount in moles times molar mass.\n2. Use m = 5.55 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 999.8658, \"unit\": \"g\"}", "dedupe_signature": "4ba9eb07c928ce32e87738ecdffcd5d61b0d9a4a9143207f5e2950128178e6db", "difficulty": "medium", "final_answer": {"answer": 999.8658, "unit": "g"}, "id": "stoich_mass_001177_glucose_5.55", "license": "Apache-2.0", "prompt": "A sample contains 5.55 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 = 5.55 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.55}, "verifier": {"formula": "moles * molar_mass", "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": "ae3afeaa5b635cc36156f279c05abf45360c9e9c6c40c90d4a9e4533dad985f7", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001185_inconsistent_74ac0b02_172619", "license": "Apache-2.0", "prompt": "In student derivation case 172619, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_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 * 1.29 * 14.\nFinal: {\"answer\": 8307.6, \"unit\": \"J\"}", "dedupe_signature": "eb6387c38396e74cfafe3ec202cadc4b7b3a063cbdbaf64dc6f9ba953fb86d2b", "difficulty": "easy", "final_answer": {"answer": 8307.6, "unit": "J"}, "id": "heat_q_001192_460_1.29_14", "license": "Apache-2.0", "prompt": "A 460 g sample has specific heat 1.29 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 = 460 * 1.29 * 14.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 14, "heat_capacity": 1.29, "mass_g": 460}, "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 325 mL to 0.325 L.\n3. Compute M = 4.86 / 0.325.\nFinal: {\"answer\": 14.9538, \"unit\": \"mol/L\"}", "dedupe_signature": "141a95230932099c9a0119fab3090dfd2fb2e533f23f704fd6cbfb20cb602295", "difficulty": "medium", "final_answer": {"answer": 14.9538, "unit": "mol/L"}, "id": "molarity_001196_4.86_325", "license": "Apache-2.0", "prompt": "A solution contains 4.86 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 = 4.86 / 0.325.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.86, "volume_ml": 325}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.9 kg and a = 8.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 145.885, \"unit\": \"N\"}", "dedupe_signature": "71abf0a4d9a9424e81b8882dc8c1362106261870a4fe91c72716d9a0e7f649c4", "difficulty": "easy", "final_answer": {"answer": 145.885, "unit": "N"}, "id": "force_001206_17.9_8.15", "license": "Apache-2.0", "prompt": "A cart has mass 17.9 kg and measured acceleration 8.15 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 = 17.9 kg and a = 8.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.15, "mass": 17.9}, "verifier": {"formula": "mass * acceleration", "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": "b6b454390842e0c452891ff757d6841ee190a1fff7779fcca11784e9c9369357", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_001223_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=2.2 mol and T=297 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": "validation", "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 = 17.1 kg and a = 2.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 35.91, \"unit\": \"N\"}", "dedupe_signature": "5b6c0deb39499c0efd09218c99925b8b0328b69b77dcdb5a1dd75bbd38f289bb", "difficulty": "easy", "final_answer": {"answer": 35.91, "unit": "N"}, "id": "force_001224_17.1_2.1", "license": "Apache-2.0", "prompt": "A cart has mass 17.1 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 = 17.1 kg and a = 2.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.1, "mass": 17.1}, "verifier": {"formula": "mass * acceleration", "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_001240(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_001240\"}", "dedupe_signature": "b73a243bf58b3a0daf6fcd83af4adaf925a908647a08a28631855f0255cc6240", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_001240"}, "id": "code_001240_finite_differences_001240", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_001240(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_001240"}, "verifier": {"function": "finite_differences_001240", "tests": ["assert finite_differences_001240([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_001240([5]) == []", "assert finite_differences_001240([]) == []"], "type": "python_tests"}}
{"category": "science_math_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 * 2.985 * 44.\nFinal: {\"answer\": 11163.9, \"unit\": \"J\"}", "dedupe_signature": "273634192f8799ebdb92c9b696d1c212832e195dd44bf10525cf44f4bbcfc323", "difficulty": "easy", "final_answer": {"answer": 11163.9, "unit": "J"}, "id": "heat_q_001246_85_2.985_44", "license": "Apache-2.0", "prompt": "A 85 g sample has specific heat 2.985 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 = 85 * 2.985 * 44.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 44, "heat_capacity": 2.985, "mass_g": 85}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=271 degrees and keep the unit as newtons.\nFinal: {\"answer\": [5.4452, -311.9525], \"unit\": \"N\"}", "dedupe_signature": "fd4c4c7e8d4212da21dcabc3b438fc740c07ae2cf9e3268bcff3b9a1b8bbcfbd", "difficulty": "medium", "final_answer": {"answer": [5.4452, -311.9525], "unit": "N"}, "id": "vector_components_001255_312_271", "license": "Apache-2.0", "prompt": "A vector has magnitude 312 N at 271 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=271 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 271, "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. 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": "1576f1fe6f52fe8e020a60a0781425e3c07035f892a177ed8090e2f2ca4d1287", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001259_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 31.5 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": "validation", "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 = 7.8^2 and multiply by 0.5 * 19.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 603.837, \"unit\": \"J\"}", "dedupe_signature": "5c29f57221fdadd34e1fde387e6077afa59417b539975ad8f8e33aadec5108f3", "difficulty": "easy", "final_answer": {"answer": 603.837, "unit": "J"}, "id": "ke_001261_19.85_7.8", "license": "Apache-2.0", "prompt": "A body of mass 19.85 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 * 19.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.85, "velocity": 7.8}, "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 = 1775 * 3.23 * 62.\nFinal: {\"answer\": 355461.5, \"unit\": \"J\"}", "dedupe_signature": "5e4ee753f0a561390578669b528277419c5f01b64be94a95355c12d1ed11101e", "difficulty": "easy", "final_answer": {"answer": 355461.5, "unit": "J"}, "id": "heat_q_001264_1775_3.23_62", "license": "Apache-2.0", "prompt": "A 1775 g sample has specific heat 3.23 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 = 1775 * 3.23 * 62.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 62, "heat_capacity": 3.23, "mass_g": 1775}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.8 kg and a = 15.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 245.69, \"unit\": \"N\"}", "dedupe_signature": "e40686ba9cb895e979bdbe0ee8473e3bff5fda7582b3b03d10e9f598fc01ae78", "difficulty": "easy", "final_answer": {"answer": 245.69, "unit": "N"}, "id": "force_001332_15.8_15.55", "license": "Apache-2.0", "prompt": "A cart has mass 15.8 kg and measured acceleration 15.55 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 = 15.8 kg and a = 15.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.55, "mass": 15.8}, "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 = 1805 * 1.725 * 53.\nFinal: {\"answer\": 165022.125, \"unit\": \"J\"}", "dedupe_signature": "7a46d76535fd0a52dd769b8b9d74cede440f4f9c95c90fa1fdec47085066bcd4", "difficulty": "easy", "final_answer": {"answer": 165022.125, "unit": "J"}, "id": "heat_q_001354_1805_1.725_53", "license": "Apache-2.0", "prompt": "A 1805 g sample has specific heat 1.725 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 = 1805 * 1.725 * 53.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 53, "heat_capacity": 1.725, "mass_g": 1805}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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": "10c060cb1bfa81b1cd37a00edd1eb87422a181f35da9583265b3c83f7e3a8f53", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001365_inconsistent_74ac0b02_454316", "license": "Apache-2.0", "prompt": "In field worksheet case 454316, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4650 mL to 4.65 L.\n3. Compute M = 2.28 / 4.65.\nFinal: {\"answer\": 0.4903, \"unit\": \"mol/L\"}", "dedupe_signature": "29e2ccc6640a900a8185d59948c13c13b09fa1cbe09ef4a39ef5b64f5f46f1f7", "difficulty": "medium", "final_answer": {"answer": 0.4903, "unit": "mol/L"}, "id": "molarity_001376_2.28_4650", "license": "Apache-2.0", "prompt": "A solution contains 2.28 mol of solute in 4650 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4650 mL to 4.65 L.\nCompute M = 2.28 / 4.65.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.28, "volume_ml": 4650}, "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=0.24 and add it to the current value.\nFinal: {\"answer\": [0.688, 1.552, 1.252], \"unit\": \"temperature_units\"}", "dedupe_signature": "e63ca789b74858ee81e4423f8dd3d75f890b9dae188b20db92f2eaa30665d298", "difficulty": "hard", "final_answer": {"answer": [0.688, 1.552, 1.252], "unit": "temperature_units"}, "id": "heat_step_001379_0.24_0.45_0.1_2.2_1.6_-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=0.45, right=-0.45; current interior values are [0.1, 2.2, 1.6]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.1, 2.2, 1.6], "left": 0.45, "r": 0.24, "right": -0.45}, "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 center_values_001402(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_001402\"}", "dedupe_signature": "d091e150c4b6eab5a14136f526865190b2ed26ac214a5c494dffdf1a4dcb011d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_001402"}, "id": "code_001402_center_values_001402", "license": "Apache-2.0", "prompt": "Write a Python function center_values_001402(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": "validation", "task_family": "python_code_generation", "variables": {"function": "center_values_001402"}, "verifier": {"function": "center_values_001402", "tests": ["out = center_values_001402([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_001402([5]) == [0]", "try:\n    center_values_001402([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.43 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 743.6464, \"unit\": \"g\"}", "dedupe_signature": "cbe7f152ad21edebe260faf752fd67b19b882b6765e1926e67b3651b85643011", "difficulty": "medium", "final_answer": {"answer": 743.6464, "unit": "g"}, "id": "stoich_mass_001411_calcium_carbonate_7.43", "license": "Apache-2.0", "prompt": "A sample contains 7.43 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 = 7.43 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.43}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R 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 * 252 / 81.7.\nFinal: {\"answer\": 23.0797, \"unit\": \"kPa\"}", "dedupe_signature": "f68d553e66571d1b7c5b894a1c36840975f1ba9f00208e75c9f69bea901dca6d", "difficulty": "medium", "final_answer": {"answer": 23.0797, "unit": "kPa"}, "id": "ideal_gas_001425_0.9_252_81.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.9 mol, T=252 K, and V=81.7 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 = 0.9 * 8.314 * 252 / 81.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.9, "temp_k": 252, "volume_l": 81.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.4 kg and a = 9.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 59.52, \"unit\": \"N\"}", "dedupe_signature": "151837e41c24ad24b3c98de085f777a707d1b00e48177ad9c648236ed894bec3", "difficulty": "easy", "final_answer": {"answer": 59.52, "unit": "N"}, "id": "force_001440_6.4_9.3", "license": "Apache-2.0", "prompt": "A cart has mass 6.4 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 = 6.4 kg and a = 9.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.3, "mass": 6.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.13, 1.36, 1.8], \"unit\": \"temperature_units\"}", "dedupe_signature": "dfd8e168c3cbdb7500c7b1a9704ef60ede1f6205bd20aa3614e5654e7abbc3d3", "difficulty": "hard", "final_answer": {"answer": [1.13, 1.36, 1.8], "unit": "temperature_units"}, "id": "heat_step_001451_0.44_0.1_2.45_1.8_0.15_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=0.1, right=2.25; current interior values are [2.45, 1.8, 0.15]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.45, 1.8, 0.15], "left": 0.1, "r": 0.44, "right": 2.25}, "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\": [-3.25, -21.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "5fe042fea1cd174dd0d8efae203a5c8768c5207e784392e1650fcd2f7534d706", "difficulty": "medium", "final_answer": {"answer": [-3.25, -21.25], "unit": "dimensionless"}, "id": "line_two_point_001454_-14.75_-7.75_-3.25_-21.25", "license": "Apache-2.0", "prompt": "A line passes through points (-14.75, 26.6875) and (-7.75, 3.9375). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -14.75, "x2": -7.75, "y1": 26.6875, "y2": 3.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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=37.2 ohm.\nFinal: {\"answer\": 196.0527, \"unit\": \"W\"}", "dedupe_signature": "9266c88d6d813457daef66ef00ee7a09ca8ebabef0593e7c952a2dfd457063b5", "difficulty": "easy", "final_answer": {"answer": 196.0527, "unit": "W"}, "id": "ohm_power_001463_85.4_37.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 37.2 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=37.2 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 37.2, "voltage": 85.4}, "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 = 3.63 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 653.9663, \"unit\": \"g\"}", "dedupe_signature": "bd1de05b5438736c66d0a83a382829fd28ea5d29ff6e43c5034dafada1f914d2", "difficulty": "medium", "final_answer": {"answer": 653.9663, "unit": "g"}, "id": "stoich_mass_001465_glucose_3.63", "license": "Apache-2.0", "prompt": "A sample contains 3.63 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 = 3.63 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.63}, "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 2 steps and round the final state.\nFinal: {\"answer\": 54.1373, \"unit\": \"state_units\"}", "dedupe_signature": "0d979c756c0cf107a1be8ab3ec7a6dee618452d531949573776cc41d27f83cb1", "difficulty": "medium", "final_answer": {"answer": 54.1373, "unit": "state_units"}, "id": "euler_decay_001467_77_0.17_0.95_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=77, step size h=0.95, 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) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 77.0, "rate": 0.17, "step": 0.95, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.65 kg and a = 1.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 0.845, \"unit\": \"N\"}", "dedupe_signature": "c5c71d851173f40e2881412946ebe9775316746e5a5e8e8c9cd33a86e9047dae", "difficulty": "easy", "final_answer": {"answer": 0.845, "unit": "N"}, "id": "force_001476_0.65_1.3", "license": "Apache-2.0", "prompt": "A cart has mass 0.65 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 = 0.65 kg and a = 1.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.3, "mass": 0.65}, "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 = 2.35 * 8.314 * 488 / 106.4.\nFinal: {\"answer\": 89.6099, \"unit\": \"kPa\"}", "dedupe_signature": "4c078332be6cff01ebf9e91e9aff26777f72363da34609002eaf16c69d3af12f", "difficulty": "medium", "final_answer": {"answer": 89.6099, "unit": "kPa"}, "id": "ideal_gas_001479_2.35_488_106.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.35 mol, T=488 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 = 2.35 * 8.314 * 488 / 106.4.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.35, "temp_k": 488, "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=33.4 V and R=99 ohm.\nFinal: {\"answer\": 11.2683, \"unit\": \"W\"}", "dedupe_signature": "2f4b700459c44599b9cf35d1d9018b8b5d91115cb3fc7e5d8d99f0cbacb2717e", "difficulty": "easy", "final_answer": {"answer": 11.2683, "unit": "W"}, "id": "ohm_power_001499_33.4_99", "license": "Apache-2.0", "prompt": "A resistor has resistance 99 ohm and voltage 33.4 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=33.4 V and R=99 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 99.0, "voltage": 33.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=99 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-17.8335, 112.5965], \"unit\": \"N\"}", "dedupe_signature": "67a981d86a6e582e486868b13deae5dc899ef3644fc46386aa2da1bb76e8aabc", "difficulty": "medium", "final_answer": {"answer": [-17.8335, 112.5965], "unit": "N"}, "id": "vector_components_001507_114_99", "license": "Apache-2.0", "prompt": "A vector has magnitude 114 N at 99 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=99 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 99, "magnitude": 114.0}, "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_001510(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_001510\"}", "dedupe_signature": "8e27329743a89810f8a7961e83b01d6e74048f1dd81107f9987e5d93b0b78f56", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_001510"}, "id": "code_001510_threshold_flags_001510", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_001510(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": "validation", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_001510"}, "verifier": {"function": "threshold_flags_001510", "tests": ["assert threshold_flags_001510([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_001510([], 5) == []", "assert threshold_flags_001510([-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": "c9b7300f31adfe46947832273b5a28e04e299024a5309349a97c14442546bfc7", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001511_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=55 and h=0.4, 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": "validation", "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=28.7 V and R=48.5 ohm.\nFinal: {\"answer\": 16.9833, \"unit\": \"W\"}", "dedupe_signature": "7e8c6cd997bf549173f104fff312a1ce269536dbb24447c6e1fd427e8d63ebff", "difficulty": "easy", "final_answer": {"answer": 16.9833, "unit": "W"}, "id": "ohm_power_001517_28.7_48.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 48.5 ohm and voltage 28.7 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=28.7 V and R=48.5 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 48.5, "voltage": 28.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 29.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "015d28476968753c415bcbe4766cd1f68ed161930997e987eefcd5e39b6e1eb0", "difficulty": "medium", "final_answer": {"answer": [7.7, 29.25], "unit": "dimensionless"}, "id": "line_two_point_001526_-18_-16.5_7.7_29.25", "license": "Apache-2.0", "prompt": "A line passes through points (-18, -109.35) and (-16.5, -97.8). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -18.0, "x2": -16.5, "y1": -109.35, "y2": -97.8}, "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. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "eb4361b6dddfa41e423f62f7bcc8372a463083935b6bb9fd655602c96d277d1a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001545_consistent_8b38953d_776138", "license": "Apache-2.0", "prompt": "In model card equation case 776138, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=968 mg, t=301 h, and T_half=24.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1939, \"unit\": \"mg\"}", "dedupe_signature": "5f7ce6686db21f4fbef1401a8e68f851c532abbda2b225d2ad8de2d7a6955608", "difficulty": "medium", "final_answer": {"answer": 0.1939, "unit": "mg"}, "id": "half_life_001626_968_24.5_301", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 968 mg. Its half-life is 24.5 hours. How many mg remain after 301 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=968 mg, t=301 h, and T_half=24.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 301.0, "half_life": 24.5, "initial_amount": 968.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "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": "cc444f20e8c63b0dc20df79230affdc4848059c06dcce211f77300c9ca4e20fc", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001635_inconsistent_56040f5d_890841", "license": "Apache-2.0", "prompt": "In model card equation case 890841, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -1.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "e02a4e012e44fa94eaa8e4b927d7bec9cfcbcdbd5d35bed6f89cb7a44c44f1f2", "difficulty": "medium", "final_answer": {"answer": [4.8, -1.75], "unit": "dimensionless"}, "id": "line_two_point_001670_5.25_13.5_4.8_-1.75", "license": "Apache-2.0", "prompt": "A line passes through points (5.25, 23.45) and (13.5, 63.05). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 5.25, "x2": 13.5, "y1": 23.45, "y2": 63.05}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.77 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 220.3188, \"unit\": \"g\"}", "dedupe_signature": "7186276ab95e9fe15d80eda674db21760ca31f2150715f27e5c988a83341e295", "difficulty": "medium", "final_answer": {"answer": 220.3188, "unit": "g"}, "id": "stoich_mass_001681_sodium_chloride_3.77", "license": "Apache-2.0", "prompt": "A sample contains 3.77 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 = 3.77 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "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 2195 mL to 2.195 L.\n3. Compute M = 3.23 / 2.195.\nFinal: {\"answer\": 1.4715, \"unit\": \"mol/L\"}", "dedupe_signature": "2cfd3c2aafe8000f7fe9791e5d22d8e6812b0c16e5758d6ea80cb904fe6dee65", "difficulty": "medium", "final_answer": {"answer": 1.4715, "unit": "mol/L"}, "id": "molarity_001682_3.23_2195", "license": "Apache-2.0", "prompt": "A solution contains 3.23 mol of solute in 2195 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2195 mL to 2.195 L.\nCompute M = 3.23 / 2.195.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.23, "volume_ml": 2195}, "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(-7.9)=9.81 and f(0.9)=-6.91.\n3. The interval width is 8.8.\nFinal: {\"answer\": 12.76, \"unit\": \"area_units\"}", "dedupe_signature": "1c50126124094b370de442c3b91901767d1e048c88bd52c51b7b23a16fd3762d", "difficulty": "medium", "final_answer": {"answer": 12.76, "unit": "area_units"}, "id": "trapz_linear_001684_-1.9_-5.2_-7.9_0.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+-5.2 from x=-7.9 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(-7.9)=9.81 and f(0.9)=-6.91.\nThe interval width is 8.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -5.2, "slope": -1.9, "x0": -7.9, "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. 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": "dc5558355738cb6a3aa7c8e2d2e32c0279b30298fe6ad3007fc225abf838706b", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001689_consistent_82e93f3d_192485", "license": "Apache-2.0", "prompt": "In model card equation case 192485, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1655 * 3.875 * 76.\nFinal: {\"answer\": 487397.5, \"unit\": \"J\"}", "dedupe_signature": "f55ae320f3a5e357825b850370f1d4a451a7542a5dfe1da054faa24d7c7027c6", "difficulty": "easy", "final_answer": {"answer": 487397.5, "unit": "J"}, "id": "heat_q_001696_1655_3.875_76", "license": "Apache-2.0", "prompt": "A 1655 g sample has specific heat 3.875 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 = 1655 * 3.875 * 76.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 76, "heat_capacity": 3.875, "mass_g": 1655}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.24 * 8.314 * 318 / 45.8.\nFinal: {\"answer\": 71.5803, \"unit\": \"kPa\"}", "dedupe_signature": "ce8d3dd41b19df916228c98bcd022f7541819017ae3eeea731fa5ff6cae21a75", "difficulty": "medium", "final_answer": {"answer": 71.5803, "unit": "kPa"}, "id": "ideal_gas_001731_1.24_318_45.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.24 mol, T=318 K, and V=45.8 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 = 1.24 * 8.314 * 318 / 45.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 1.24, "temp_k": 318, "volume_l": 45.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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": "63eac0d01d1f88d737ba8dd8d4ce397af430a4d0737300d54dcbab9631bfb8bb", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001745_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 4169 items and budget 16580, 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": "validation", "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 = 12.65 kg and a = 1.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 22.1375, \"unit\": \"N\"}", "dedupe_signature": "f4141a2325816f9f1c0398fec739a362bc99fed10252af74da480c364838829f", "difficulty": "easy", "final_answer": {"answer": 22.1375, "unit": "N"}, "id": "force_001746_12.65_1.75", "license": "Apache-2.0", "prompt": "A cart has mass 12.65 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 = 12.65 kg and a = 1.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.75, "mass": 12.65}, "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=68 degrees through the sine of 2 theta.\n3. Substitute v=71.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 363.0181, \"unit\": \"m\"}", "dedupe_signature": "4a936f387d1f630164450e4920b5076771a495c32756b7a882758225e69c4d78", "difficulty": "medium", "final_answer": {"answer": 363.0181, "unit": "m"}, "id": "projectile_range_001766_71.6_68", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71.6 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=71.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 68, "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4270 mL to 4.27 L.\n3. Compute M = 3.24 / 4.27.\nFinal: {\"answer\": 0.7588, \"unit\": \"mol/L\"}", "dedupe_signature": "8d36d5b43f76cba815aab8346905ed6a4e437b29fcabbb73c01e2a4fd61e8bf4", "difficulty": "medium", "final_answer": {"answer": 0.7588, "unit": "mol/L"}, "id": "molarity_001772_3.24_4270", "license": "Apache-2.0", "prompt": "A solution contains 3.24 mol of solute in 4270 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4270 mL to 4.27 L.\nCompute M = 3.24 / 4.27.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.24, "volume_ml": 4270}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.35^2 and multiply by 0.5 * 25.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3381.6296, \"unit\": \"J\"}", "dedupe_signature": "e1aa1ccf2f2c33ad38268be810f7a12ea5cc2df08462fb101835d6dda52551e2", "difficulty": "easy", "final_answer": {"answer": 3381.6296, "unit": "J"}, "id": "ke_001783_25.3_16.35", "license": "Apache-2.0", "prompt": "A body of mass 25.3 kg moves at 16.35 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 = 16.35^2 and multiply by 0.5 * 25.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.3, "velocity": 16.35}, "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=629 mg, t=359.5 h, and T_half=93 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 43.1511, \"unit\": \"mg\"}", "dedupe_signature": "202a9636665597106edc9b2b5da239f3489fb02438ce62e73f5f0090d50acc99", "difficulty": "medium", "final_answer": {"answer": 43.1511, "unit": "mg"}, "id": "half_life_001806_629_93_359.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 629 mg. Its half-life is 93 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=629 mg, t=359.5 h, and T_half=93 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 359.5, "half_life": 93.0, "initial_amount": 629.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "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": "7d77e463f232773d80f440aa098f72690eba0600a5a121cda2d078f98b26b2c2", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001817_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 2336 items and budget 77505, 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": "validation", "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. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -35.5 + 273.15.\nFinal: {\"answer\": 237.65, \"unit\": \"K\"}", "dedupe_signature": "013a1a764560f95667f842b52b5e6c2a291e33582031189c4770d23129f07240", "difficulty": "easy", "final_answer": {"answer": 237.65, "unit": "K"}, "id": "unit_convert_001830_c_to_k_-35.5", "license": "Apache-2.0", "prompt": "Convert -35.5 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 -35.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": -35.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 22.5^2 and multiply by 0.5 * 3.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 847.9688, \"unit\": \"J\"}", "dedupe_signature": "264b0b0adcc1e530ecd83d13c7f18ea5ce0a4c70d955461d6e31f6f625506bb7", "difficulty": "easy", "final_answer": {"answer": 847.9688, "unit": "J"}, "id": "ke_001837_3.35_22.5", "license": "Apache-2.0", "prompt": "A body of mass 3.35 kg moves at 22.5 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 = 22.5^2 and multiply by 0.5 * 3.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 3.35, "velocity": 22.5}, "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=34 V and R=89 ohm.\nFinal: {\"answer\": 12.9888, \"unit\": \"W\"}", "dedupe_signature": "7d2fd01386bc48b8c5ce21f40fb53580be7f66514b37e8ac0ea32e63d7eef9a7", "difficulty": "easy", "final_answer": {"answer": 12.9888, "unit": "W"}, "id": "ohm_power_001841_34_89", "license": "Apache-2.0", "prompt": "A resistor has resistance 89 ohm and voltage 34 V across it. Compute the dissipated power 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 V and R=89 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 89.0, "voltage": 34.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.05 kg and a = 6.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 21.1975, \"unit\": \"N\"}", "dedupe_signature": "e317e859bd2cac23fd1246da8131ac6d70a7c9c6bf1b22fae51d14f2f9c25753", "difficulty": "easy", "final_answer": {"answer": 21.1975, "unit": "N"}, "id": "force_001872_3.05_6.95", "license": "Apache-2.0", "prompt": "A cart has mass 3.05 kg and measured acceleration 6.95 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 = 3.05 kg and a = 6.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.95, "mass": 3.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4350 mL to 4.35 L.\n3. Compute M = 2.955 / 4.35.\nFinal: {\"answer\": 0.6793, \"unit\": \"mol/L\"}", "dedupe_signature": "d755cec8bca8d163a05d7dfea9f4806bb9653111c7311f0846ad3ff8c41cb97a", "difficulty": "medium", "final_answer": {"answer": 0.6793, "unit": "mol/L"}, "id": "molarity_001880_2.955_4350", "license": "Apache-2.0", "prompt": "A solution contains 2.955 mol of solute in 4350 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4350 mL to 4.35 L.\nCompute M = 2.955 / 4.35.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.955, "volume_ml": 4350}, "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 26634.0 / 1000.\nFinal: {\"answer\": 26.634, \"unit\": \"kg\"}", "dedupe_signature": "378aa93955d16b651bf8d5a048e4388e4668d7fb381a9047043dd639d7d2b69f", "difficulty": "easy", "final_answer": {"answer": 26.634, "unit": "kg"}, "id": "unit_convert_001884_g_to_kg_26634", "license": "Apache-2.0", "prompt": "Convert 26634 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 26634.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 26634.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 295 * 3.35 * 5.\nFinal: {\"answer\": 4941.25, \"unit\": \"J\"}", "dedupe_signature": "25f95b2afe886381d8f26077392281445640398c25bbc2389e5f7e3d6b051f4c", "difficulty": "easy", "final_answer": {"answer": 4941.25, "unit": "J"}, "id": "heat_q_001930_295_3.35_5", "license": "Apache-2.0", "prompt": "A 295 g sample has specific heat 3.35 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 = 295 * 3.35 * 5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 3.35, "mass_g": 295}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 310 * 4.39 * 103.\nFinal: {\"answer\": 140172.7, \"unit\": \"J\"}", "dedupe_signature": "60ba72d31f9eb0425f3f17b054297eff0f6d842f73fb39aa5120d0345fc42390", "difficulty": "easy", "final_answer": {"answer": 140172.7, "unit": "J"}, "id": "heat_q_001948_310_4.39_103", "license": "Apache-2.0", "prompt": "A 310 g sample has specific heat 4.39 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 = 310 * 4.39 * 103.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 103, "heat_capacity": 4.39, "mass_g": 310}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=40.2 V and R=134.9 ohm.\nFinal: {\"answer\": 11.9795, \"unit\": \"W\"}", "dedupe_signature": "a7091663fd83962c4d85e36c896815155f4d8dbe193164f242926c23f817736c", "difficulty": "easy", "final_answer": {"answer": 11.9795, "unit": "W"}, "id": "ohm_power_001949_40.2_134.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 134.9 ohm and voltage 40.2 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=40.2 V and R=134.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 134.9, "voltage": 40.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -20.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "77c93ec9c61a934d78bef2ceca4b39328e1a93bd9a48fed94798fcd76b0f6160", "difficulty": "medium", "final_answer": {"answer": [7.85, -20.25], "unit": "dimensionless"}, "id": "line_two_point_001958_14.25_20.75_7.85_-20.25", "license": "Apache-2.0", "prompt": "A line passes through points (14.25, 91.6125) and (20.75, 142.637). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "linear_modeling", "variables": {"x1": 14.25, "x2": 20.75, "y1": 91.6125, "y2": 142.6375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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=104.3 ohm.\nFinal: {\"answer\": 347.5758, \"unit\": \"W\"}", "dedupe_signature": "bc08cd970f5d2adb0a577bd6a1cd3b60ac0ec1823e1217407b208d145046d2b1", "difficulty": "easy", "final_answer": {"answer": 347.5758, "unit": "W"}, "id": "ohm_power_001967_190.4_104.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 104.3 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=104.3 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 104.3, "voltage": 190.4}, "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 = 0.98 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 176.5529, \"unit\": \"g\"}", "dedupe_signature": "f30f0d1bd060dc01f1d174910b16dfe302b558eac239530534267156ee3fc694", "difficulty": "medium", "final_answer": {"answer": 176.5529, "unit": "g"}, "id": "stoich_mass_001969_glucose_0.98", "license": "Apache-2.0", "prompt": "A sample contains 0.98 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 = 0.98 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.98}, "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(-9.7)=-52.52 and f(-5.6)=-25.46.\n3. The interval width is 4.1.\nFinal: {\"answer\": -159.859, \"unit\": \"area_units\"}", "dedupe_signature": "7d8ab1135c2749091d5613fa21466871faebad1336530c8fd5cc2c7547160122", "difficulty": "medium", "final_answer": {"answer": -159.859, "unit": "area_units"}, "id": "trapz_linear_001972_6.6_11.5_-9.7_-5.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+11.5 from x=-9.7 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(-9.7)=-52.52 and f(-5.6)=-25.46.\nThe interval width is 4.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 11.5, "slope": 6.6, "x0": -9.7, "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. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.66 * 8.314 * 378 / 40.3.\nFinal: {\"answer\": 51.4684, \"unit\": \"kPa\"}", "dedupe_signature": "13d425f276c3347fffad88e065b0a70fbec543f1803ea140ba0c27dd059c154f", "difficulty": "medium", "final_answer": {"answer": 51.4684, "unit": "kPa"}, "id": "ideal_gas_002001_0.66_378_40.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.66 mol, T=378 K, and V=40.3 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 = 0.66 * 8.314 * 378 / 40.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.66, "temp_k": 378, "volume_l": 40.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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": "1479933e97c91688052513acb50372e2fda0bc117a50b9e822fe0249f62745c4", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002031_consistent_8b38953d_174408", "license": "Apache-2.0", "prompt": "In quality-control check case 174408, 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": "validation", "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: 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": "328812784ce9ef4e1cd3c0d5126a4f9967fe71f7f76e5f0ab4ced9ac84e5280d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002033_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 285 items and budget 38560, 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": "validation", "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. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.28, 0.11, 1.39], \"unit\": \"temperature_units\"}", "dedupe_signature": "e24cd780cccbf14607beb248468f3119d09d7797f9f11e1e17c99bdba472bfb7", "difficulty": "hard", "final_answer": {"answer": [1.28, 0.11, 1.39], "unit": "temperature_units"}, "id": "heat_step_002063_0.4_1.7_0.9_1.05_-1.15_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=1.7, right=3; current interior values are [0.9, 1.05, -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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.9, 1.05, -1.15], "left": 1.7, "r": 0.4, "right": 3.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.76 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 136.9186, \"unit\": \"g\"}", "dedupe_signature": "a3b8f365d8d08009bc7bc388171da2aa670ab1e96555b42a9b616d88c545fe41", "difficulty": "medium", "final_answer": {"answer": 136.9186, "unit": "g"}, "id": "stoich_mass_002077_glucose_0.76", "license": "Apache-2.0", "prompt": "A sample contains 0.76 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 = 0.76 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.76}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 10.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "be7a71f7a70f69c7e4fdae9ac7f4dff30ea23f73eb1996c991081742559de258", "difficulty": "medium", "final_answer": {"answer": [1.55, 10.75], "unit": "dimensionless"}, "id": "line_two_point_002084_16.5_22.25_1.55_10.75", "license": "Apache-2.0", "prompt": "A line passes through points (16.5, 36.325) and (22.25, 45.2375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "linear_modeling", "variables": {"x1": 16.5, "x2": 22.25, "y1": 36.325, "y2": 45.237500000000004}, "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_002086(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_002086\"}", "dedupe_signature": "e475b2298fa547205a0ff42ebf5b78ea8d590aae52ecc22dc017cee1bc604d7d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_002086"}, "id": "code_002086_running_total_002086", "license": "Apache-2.0", "prompt": "Write a Python function running_total_002086(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_002086"}, "verifier": {"function": "running_total_002086", "tests": ["assert running_total_002086([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_002086(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_002086([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.5^2 and multiply by 0.5 * 5.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1236.5187, \"unit\": \"J\"}", "dedupe_signature": "f245e6947e1a3919f89c7e74904dad96d5bc46a1b6815ad50c078d07ef2a622c", "difficulty": "easy", "final_answer": {"answer": 1236.5187, "unit": "J"}, "id": "ke_002089_5.35_21.5", "license": "Apache-2.0", "prompt": "A body of mass 5.35 kg moves at 21.5 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 = 21.5^2 and multiply by 0.5 * 5.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.35, "velocity": 21.5}, "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 = 1080 * 4.91 * 2.\nFinal: {\"answer\": 10605.6, \"unit\": \"J\"}", "dedupe_signature": "ae85b130ccdd5ed260b019f6d02439db1eedd19945cd96079699a2b86a5b2389", "difficulty": "easy", "final_answer": {"answer": 10605.6, "unit": "J"}, "id": "heat_q_002110_1080_4.91_2", "license": "Apache-2.0", "prompt": "A 1080 g sample has specific heat 4.91 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 = 1080 * 4.91 * 2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 2, "heat_capacity": 4.91, "mass_g": 1080}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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_002158(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002158\"}", "dedupe_signature": "456fd1603710dd34223ec658a0ee712d5c6810f14d482893c39ccf83d5457b1c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002158"}, "id": "code_002158_finite_differences_002158", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002158(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002158"}, "verifier": {"function": "finite_differences_002158", "tests": ["assert finite_differences_002158([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002158([5]) == []", "assert finite_differences_002158([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.9 kg and a = 12.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 113.92, \"unit\": \"N\"}", "dedupe_signature": "f18e2e1e5ef2491948a4441b8da7bae1cd2435899b97d45bbc88892502118aae", "difficulty": "easy", "final_answer": {"answer": 113.92, "unit": "N"}, "id": "force_002214_8.9_12.8", "license": "Apache-2.0", "prompt": "A cart has mass 8.9 kg and measured acceleration 12.8 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 = 8.9 kg and a = 12.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.8, "mass": 8.9}, "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=161.6 V and R=75.6 ohm.\nFinal: {\"answer\": 345.4307, \"unit\": \"W\"}", "dedupe_signature": "de6fbe0b084fbadf9cb9b91108b1b0ae81260e29d7792859484226760bb74b2e", "difficulty": "easy", "final_answer": {"answer": 345.4307, "unit": "W"}, "id": "ohm_power_002219_161.6_75.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 75.6 ohm and voltage 161.6 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=161.6 V and R=75.6 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 75.6, "voltage": 161.6}, "verifier": {"formula": "voltage ** 2 / resistance", "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": "1950c239f0d9dd341d309a740c6e8ac2d976515e14708430f49696322551eee5", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002231_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=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": "validation", "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. The function contract has a 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_002248(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_002248\"}", "dedupe_signature": "eecc4727812cd88375faf126d2075cfefcbcf7aac9e250cb06e09ebc53aa26c5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_002248"}, "id": "code_002248_running_total_002248", "license": "Apache-2.0", "prompt": "Write a Python function running_total_002248(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_002248"}, "verifier": {"function": "running_total_002248", "tests": ["assert running_total_002248([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_002248(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_002248([]) == []"], "type": "python_tests"}}
{"category": "science_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": "e446eeb14f2e2d9d911f5c8e477cf100a4a2ec0665a229065ef558b5ef2d5f56", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_002249_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 [-0.2, 1.55, 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": "validation", "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 the ideal gas law P V = n R 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 * 332 / 17.8.\nFinal: {\"answer\": 389.226, \"unit\": \"kPa\"}", "dedupe_signature": "73dfc2116e5d80d6a65716b456f756580aaf5ab9fc9214e54dd4415e495d1bd3", "difficulty": "medium", "final_answer": {"answer": 389.226, "unit": "kPa"}, "id": "ideal_gas_002253_2.51_332_17.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.51 mol, T=332 K, and V=17.8 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 = 2.51 * 8.314 * 332 / 17.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.51, "temp_k": 332, "volume_l": 17.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"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\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "482be59cc5ab08ae3af736b6c246d485d8976bd05886db2fe12c718926013b6a", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002313_2.5_0.38_1.95_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.38 y with y(0)=2.5, step size h=1.95, 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) = -0.38 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 2.5, "rate": 0.38, "step": 1.95, "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 14066.0 / 1000.\nFinal: {\"answer\": 14.066, \"unit\": \"kg\"}", "dedupe_signature": "bbb118f5b9a86a3f8eb413fa478cdd15c0214daff14e39d9c4f2218f9398445f", "difficulty": "easy", "final_answer": {"answer": 14.066, "unit": "kg"}, "id": "unit_convert_002334_g_to_kg_14066", "license": "Apache-2.0", "prompt": "Convert 14066 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 14066.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 14066.0}, "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\": [-1.9, 10.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7be052b7dd2f0e7262627f1706d17861017f1cb5a7f687853271a72ddf46f67b", "difficulty": "medium", "final_answer": {"answer": [-1.9, 10.25], "unit": "dimensionless"}, "id": "line_two_point_002336_6.5_7_-1.9_10.25", "license": "Apache-2.0", "prompt": "A line passes through points (6.5, -2.1) and (7, -3.05). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 6.5, "x2": 7.0, "y1": -2.0999999999999996, "y2": -3.049999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "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=39.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 90.7483, \"unit\": \"m\"}", "dedupe_signature": "8bd67bd5d4e7eb6dd2fcd2c64e5c6a810d6b08ac08d5d2585b292cb92b37de4c", "difficulty": "medium", "final_answer": {"answer": 90.7483, "unit": "m"}, "id": "projectile_range_002342_39.9_17", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 39.9 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=39.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 17, "gravity": 9.81, "speed": 39.9}, "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 = 1720 * 4.075 * 2.\nFinal: {\"answer\": 14018.0, \"unit\": \"J\"}", "dedupe_signature": "183dec42787b011f139f15366aedff3e1a0db6791b400ad1d441b977959b9c88", "difficulty": "easy", "final_answer": {"answer": 14018.0, "unit": "J"}, "id": "heat_q_002344_1720_4.075_2", "license": "Apache-2.0", "prompt": "A 1720 g sample has specific heat 4.075 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 = 1720 * 4.075 * 2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 2, "heat_capacity": 4.075, "mass_g": 1720}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"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 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "faf12622c687d29de097c07e5b67144ddabb2631a402711e1fb027f33be9e003", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002349_77.5_0.58_1.4_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.58 y with y(0)=77.5, step size h=1.4, 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) = -0.58 y, so each step multiplies y by 1 - h*0.58.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 77.5, "rate": 0.58, "step": 1.4, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.8^2 and multiply by 0.5 * 20.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 32.886, \"unit\": \"J\"}", "dedupe_signature": "96d5802e11224a06d62b6d70eedfbc4b0fda6f1f1ece2b01f8210608f73bc26a", "difficulty": "easy", "final_answer": {"answer": 32.886, "unit": "J"}, "id": "ke_002359_20.3_1.8", "license": "Apache-2.0", "prompt": "A body of mass 20.3 kg moves at 1.8 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 = 1.8^2 and multiply by 0.5 * 20.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.3, "velocity": 1.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2090 mL to 2.09 L.\n3. Compute M = 0.025 / 2.09.\nFinal: {\"answer\": 0.012, \"unit\": \"mol/L\"}", "dedupe_signature": "76919dafa5b8746e0b5a2e8e0590a800ccb03c7219c81d89006b213ae4b610a8", "difficulty": "medium", "final_answer": {"answer": 0.012, "unit": "mol/L"}, "id": "molarity_002366_0.025_2090", "license": "Apache-2.0", "prompt": "A solution contains 0.025 mol of solute in 2090 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2090 mL to 2.09 L.\nCompute M = 0.025 / 2.09.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 0.025, "volume_ml": 2090}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.96 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 231.4224, \"unit\": \"g\"}", "dedupe_signature": "26385d76c07b9ea655bdff12567b33bba8c684a98b92131c3c608cf47becbcf8", "difficulty": "medium", "final_answer": {"answer": 231.4224, "unit": "g"}, "id": "stoich_mass_002383_sodium_chloride_3.96", "license": "Apache-2.0", "prompt": "A sample contains 3.96 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 = 3.96 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.96}, "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) = -0.78 y, so each step multiplies y by 1 - h*0.78.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.2633, \"unit\": \"state_units\"}", "dedupe_signature": "2afce9d486421cf68aa6badfae765340f44bb51bf9ab1ba78592f686d43d66f1", "difficulty": "medium", "final_answer": {"answer": 0.2633, "unit": "state_units"}, "id": "euler_decay_002403_60.5_0.78_0.5_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.78 y with y(0)=60.5, step size h=0.5, 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) = -0.78 y, so each step multiplies y by 1 - h*0.78.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 60.5, "rate": 0.78, "step": 0.5, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=146.6 V and R=183.5 ohm.\nFinal: {\"answer\": 117.1202, \"unit\": \"W\"}", "dedupe_signature": "7bae0dfa6ce3d64639becfb59f199be29b7f2f09be36397a844611b98489038c", "difficulty": "easy", "final_answer": {"answer": 117.1202, "unit": "W"}, "id": "ohm_power_002417_146.6_183.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 183.5 ohm and voltage 146.6 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=146.6 V and R=183.5 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 183.5, "voltage": 146.6}, "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 = 4.91 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 216.0891, \"unit\": \"g\"}", "dedupe_signature": "1c03cf8109f063403b6b2ab0090acd8d42fcc0a2b17b0d6d1c0242e4f69bfbdf", "difficulty": "medium", "final_answer": {"answer": 216.0891, "unit": "g"}, "id": "stoich_mass_002419_carbon_dioxide_4.91", "license": "Apache-2.0", "prompt": "A sample contains 4.91 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 = 4.91 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.91}, "verifier": {"formula": "moles * molar_mass", "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_002428(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_002428\"}", "dedupe_signature": "8070f3938d7f8b1de5f6c0c822b4918044b6e60773e6978e32b22aad2bb49d4e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_002428"}, "id": "code_002428_clamp_002428", "license": "Apache-2.0", "prompt": "Write a Python function clamp_002428(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": "validation", "task_family": "python_code_generation", "variables": {"function": "clamp_002428"}, "verifier": {"function": "clamp_002428", "tests": ["assert clamp_002428(5, 0, 10) == 5", "assert clamp_002428(-2, 0, 10) == 0", "assert clamp_002428(12, 0, 10) == 10", "try:\n    clamp_002428(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=7 degrees through the sine of 2 theta.\n3. Substitute v=64.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 103.2321, \"unit\": \"m\"}", "dedupe_signature": "6e5d852fd18eb3628d84baccddcb8843642594de57b79041f1814b0fe4a942f7", "difficulty": "medium", "final_answer": {"answer": 103.2321, "unit": "m"}, "id": "projectile_range_002432_64.7_7", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 64.7 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=64.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 7, "gravity": 9.81, "speed": 64.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.22 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 622.5411, \"unit\": \"g\"}", "dedupe_signature": "bb0fb89e009058b874847aa190f4570e11a8662d49f7d9e6ee90b4797e9269c6", "difficulty": "medium", "final_answer": {"answer": 622.5411, "unit": "g"}, "id": "stoich_mass_002437_calcium_carbonate_6.22", "license": "Apache-2.0", "prompt": "A sample contains 6.22 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 = 6.22 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "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 1595 mL to 1.595 L.\n3. Compute M = 3.68 / 1.595.\nFinal: {\"answer\": 2.3072, \"unit\": \"mol/L\"}", "dedupe_signature": "811974c093d2b3c864492254f63f58813039c4e35f495461d591ae5a4ad40f88", "difficulty": "medium", "final_answer": {"answer": 2.3072, "unit": "mol/L"}, "id": "molarity_002438_3.68_1595", "license": "Apache-2.0", "prompt": "A solution contains 3.68 mol of solute in 1595 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1595 mL to 1.595 L.\nCompute M = 3.68 / 1.595.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.68, "volume_ml": 1595}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.7 kg and a = 14.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 153.545, \"unit\": \"N\"}", "dedupe_signature": "1bafde831aa0766bbfb6cb18f3008a6e065661dde050db425987e2946b6a0d71", "difficulty": "easy", "final_answer": {"answer": 153.545, "unit": "N"}, "id": "force_002448_10.7_14.35", "license": "Apache-2.0", "prompt": "A cart has mass 10.7 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 = 10.7 kg and a = 14.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.35, "mass": 10.7}, "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=491 mg, t=7.5 h, and T_half=64.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 452.9789, \"unit\": \"mg\"}", "dedupe_signature": "288fce48de190814cc83265dbed47271a716f963e0d5f056b3f7736c12124e2b", "difficulty": "medium", "final_answer": {"answer": 452.9789, "unit": "mg"}, "id": "half_life_002454_491_64.5_7.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 491 mg. Its half-life is 64.5 hours. How many mg remain after 7.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=491 mg, t=7.5 h, and T_half=64.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 7.5, "half_life": 64.5, "initial_amount": 491.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 290 * 2.66 * 88.\nFinal: {\"answer\": 67883.2, \"unit\": \"J\"}", "dedupe_signature": "f28ea1325714401b7d3c4d1fc9a5f33707dadb90e80f3b2289f2ad5a1dfc3307", "difficulty": "easy", "final_answer": {"answer": 67883.2, "unit": "J"}, "id": "heat_q_002470_290_2.66_88", "license": "Apache-2.0", "prompt": "A 290 g sample has specific heat 2.66 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 = 290 * 2.66 * 88.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 88, "heat_capacity": 2.66, "mass_g": 290}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "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=48.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 208.5135, \"unit\": \"m\"}", "dedupe_signature": "69826de06a0f553a3a295de876b2af5b87655964d9ae30c2cd036750f5cb9f4e", "difficulty": "medium", "final_answer": {"answer": 208.5135, "unit": "m"}, "id": "projectile_range_002486_48.6_60", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 48.6 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=48.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 60, "gravity": 9.81, "speed": 48.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.063, -1.613, 1.991], \"unit\": \"temperature_units\"}", "dedupe_signature": "6b7cce87275becb98993d0cea3de7904382d1fabc9261cfdd2218dd1e3e0edfd", "difficulty": "hard", "final_answer": {"answer": [-0.063, -1.613, 1.991], "unit": "temperature_units"}, "id": "heat_step_002495_0.06_0.95_0.0_-2.0_2.45_-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=0.95, right=-0.75; current interior values are [0.0, -2.0, 2.45]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.0, -2.0, 2.45], "left": 0.95, "r": 0.06, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18 kg and a = 9.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 171.9, \"unit\": \"N\"}", "dedupe_signature": "c9e998275b6680aacae63596e14acb601902d34a381d5a98e8cda93ecbbef372", "difficulty": "easy", "final_answer": {"answer": 171.9, "unit": "N"}, "id": "force_002502_18_9.55", "license": "Apache-2.0", "prompt": "A cart has mass 18 kg and measured acceleration 9.55 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 = 18 kg and a = 9.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.55, "mass": 18.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"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 2 steps and round the final state.\nFinal: {\"answer\": 2.8072, \"unit\": \"state_units\"}", "dedupe_signature": "2ad54bb145128ab8a80fbc4580ac34f7af609e082caccbda5b50ce899ce28da4", "difficulty": "medium", "final_answer": {"answer": 2.8072, "unit": "state_units"}, "id": "euler_decay_002529_58_0.4_1.95_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.4 y with y(0)=58, 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) = -0.4 y, so each step multiplies y by 1 - h*0.4.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 58.0, "rate": 0.4, "step": 1.95, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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 4 steps and round the final state.\nFinal: {\"answer\": 34.2245, \"unit\": \"state_units\"}", "dedupe_signature": "7b6f345d60f4d23a0828bda266bd3a9a6f66bdcb4503fdb64ce534e0f22750a5", "difficulty": "medium", "final_answer": {"answer": 34.2245, "unit": "state_units"}, "id": "euler_decay_002547_38.5_0.02_1.45_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.02 y with y(0)=38.5, step size h=1.45, 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) = -0.02 y, so each step multiplies y by 1 - h*0.02.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 38.5, "rate": 0.02, "step": 1.45, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.1^2 and multiply by 0.5 * 25.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4678.6883, \"unit\": \"J\"}", "dedupe_signature": "45ee39f81586e40eae453be6bd77e918fe27b48127dfe001f25b39eb633e029e", "difficulty": "easy", "final_answer": {"answer": 4678.6883, "unit": "J"}, "id": "ke_002557_25.65_19.1", "license": "Apache-2.0", "prompt": "A body of mass 25.65 kg moves at 19.1 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 = 19.1^2 and multiply by 0.5 * 25.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.65, "velocity": 19.1}, "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=154.9 V and R=159.3 ohm.\nFinal: {\"answer\": 150.6215, \"unit\": \"W\"}", "dedupe_signature": "8a02719d4e617c88bbb071ec182ea28b070c569a1de4d103c5a92083e7489488", "difficulty": "easy", "final_answer": {"answer": 150.6215, "unit": "W"}, "id": "ohm_power_002561_154.9_159.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 159.3 ohm and voltage 154.9 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=154.9 V and R=159.3 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 159.3, "voltage": 154.9}, "verifier": {"formula": "voltage ** 2 / resistance", "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": "b49dcc97fb65eab0f1b20b1db9ed35988c7c9b28397d77464ed265549741bb8b", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002571_consistent_03f5e041_712839", "license": "Apache-2.0", "prompt": "In sensor calibration case 712839, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"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 = 3.6 / 3.98.\nFinal: {\"answer\": 0.9045, \"unit\": \"mol/L\"}", "dedupe_signature": "a9c72b192a2920b37c568ba41fc73c8bb81dc0506fdcb76cbf86a2baf8959cca", "difficulty": "medium", "final_answer": {"answer": 0.9045, "unit": "mol/L"}, "id": "molarity_002582_3.6_3980", "license": "Apache-2.0", "prompt": "A solution contains 3.6 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 = 3.6 / 3.98.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.6, "volume_ml": 3980}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.15 kg and a = 15.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 65.7775, \"unit\": \"N\"}", "dedupe_signature": "9b0825319033ec78b84733a8c269f4f4678287f95dbb9a481cf9557f5759dc82", "difficulty": "easy", "final_answer": {"answer": 65.7775, "unit": "N"}, "id": "force_002592_4.15_15.85", "license": "Apache-2.0", "prompt": "A cart has mass 4.15 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 = 4.15 kg and a = 15.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.85, "mass": 4.15}, "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 = 300 * 1.65 * 37.\nFinal: {\"answer\": 18315.0, \"unit\": \"J\"}", "dedupe_signature": "38a8a45bb2f7c72c7a87081431b265ce12a6df24d82f26761bb0804358cf1efb", "difficulty": "easy", "final_answer": {"answer": 18315.0, "unit": "J"}, "id": "heat_q_002596_300_1.65_37", "license": "Apache-2.0", "prompt": "A 300 g sample has specific heat 1.65 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 = 300 * 1.65 * 37.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 37, "heat_capacity": 1.65, "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=170.2 V and R=75.9 ohm.\nFinal: {\"answer\": 381.6606, \"unit\": \"W\"}", "dedupe_signature": "240449b5741702096280d09bf6f0020ce84dc55394ef0706cb233c3631056068", "difficulty": "easy", "final_answer": {"answer": 381.6606, "unit": "W"}, "id": "ohm_power_002597_170.2_75.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 75.9 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=75.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 75.9, "voltage": 170.2}, "verifier": {"formula": "voltage ** 2 / resistance", "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 14575.0 / 1000.\nFinal: {\"answer\": 14.575, \"unit\": \"kg\"}", "dedupe_signature": "9ebbf5223be7c42e5b82598cf4e48d14fdc299196322d3ba394e3558bea50685", "difficulty": "easy", "final_answer": {"answer": 14.575, "unit": "kg"}, "id": "unit_convert_002604_g_to_kg_14575", "license": "Apache-2.0", "prompt": "Convert 14575 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 14575.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 14575.0}, "verifier": {"formula": "value / 1000", "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_002626(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_002626\"}", "dedupe_signature": "d1f340c4ff8aa548cc71efcb68b63b8b38ad4f966e6d808682b783c4efc6cb4e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_002626"}, "id": "code_002626_running_total_002626", "license": "Apache-2.0", "prompt": "Write a Python function running_total_002626(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_002626"}, "verifier": {"function": "running_total_002626", "tests": ["assert running_total_002626([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_002626(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_002626([]) == []"], "type": "python_tests"}}
{"category": "science_math_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 * 0.865 * 68.\nFinal: {\"answer\": 94700.2, \"unit\": \"J\"}", "dedupe_signature": "a0d09018d00c8c038dd290f827b0e46b6eba7d78ed8b150c07b528c5d2f95f28", "difficulty": "easy", "final_answer": {"answer": 94700.2, "unit": "J"}, "id": "heat_q_002632_1610_0.865_68", "license": "Apache-2.0", "prompt": "A 1610 g sample has specific heat 0.865 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 = 1610 * 0.865 * 68.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 68, "heat_capacity": 0.865, "mass_g": 1610}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.75 kg and a = 15.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 73.625, \"unit\": \"N\"}", "dedupe_signature": "4610781f9410969eece73ebc7392ec595103ba0d063ce30df4a2a1f797a7ad6d", "difficulty": "easy", "final_answer": {"answer": 73.625, "unit": "N"}, "id": "force_002682_4.75_15.5", "license": "Apache-2.0", "prompt": "A cart has mass 4.75 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 = 4.75 kg and a = 15.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.5, "mass": 4.75}, "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 = 1.67 * 8.314 * 567 / 101.3.\nFinal: {\"answer\": 77.7142, \"unit\": \"kPa\"}", "dedupe_signature": "acc92a2571b0adaf3cf3de7b7a84a51774a1f128730dca015b5efdc9cca6536c", "difficulty": "medium", "final_answer": {"answer": 77.7142, "unit": "kPa"}, "id": "ideal_gas_002685_1.67_567_101.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.67 mol, T=567 K, and V=101.3 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 = 1.67 * 8.314 * 567 / 101.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 1.67, "temp_k": 567, "volume_l": 101.3}, "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 = 40 * 4.47 * 79.\nFinal: {\"answer\": 14125.2, \"unit\": \"J\"}", "dedupe_signature": "8cf8e92af203ffabe973f3c4368127ca13f236e6e1b5fae84444ad3f6de067da", "difficulty": "easy", "final_answer": {"answer": 14125.2, "unit": "J"}, "id": "heat_q_002686_40_4.47_79", "license": "Apache-2.0", "prompt": "A 40 g sample has specific heat 4.47 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 = 40 * 4.47 * 79.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 4.47, "mass_g": 40}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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(0.4)=1.5 and f(1.3)=0.6.\n3. The interval width is 0.9.\nFinal: {\"answer\": 0.945, \"unit\": \"area_units\"}", "dedupe_signature": "3add807c9dc7f8e26c02e1f649235a6cce1917bbcb5ac9f56c92920318c178dc", "difficulty": "medium", "final_answer": {"answer": 0.945, "unit": "area_units"}, "id": "trapz_linear_002692_-1_1.9_0.4_1.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1x+1.9 from x=0.4 to x=1.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.4)=1.5 and f(1.3)=0.6.\nThe interval width is 0.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 1.9, "slope": -1.0, "x0": 0.4, "x1": 1.3}, "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\": [-9.0, 19.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "3ed4983c6e68aa790514bad740c5bce1e85ba5d851a7f729fd93b7575d105e67", "difficulty": "medium", "final_answer": {"answer": [-9.0, 19.0], "unit": "dimensionless"}, "id": "line_two_point_002696_-6.75_2.75_-9_19", "license": "Apache-2.0", "prompt": "A line passes through points (-6.75, 79.75) and (2.75, -5.75). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -6.75, "x2": 2.75, "y1": 79.75, "y2": -5.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 595 * 2.57 * 66.\nFinal: {\"answer\": 100923.9, \"unit\": \"J\"}", "dedupe_signature": "30bc1fdab50e47f30d814899fb8e383ac93fa45309090f43246bd870b136e3e4", "difficulty": "easy", "final_answer": {"answer": 100923.9, "unit": "J"}, "id": "heat_q_002704_595_2.57_66", "license": "Apache-2.0", "prompt": "A 595 g sample has specific heat 2.57 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 = 595 * 2.57 * 66.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 66, "heat_capacity": 2.57, "mass_g": 595}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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 -25.0 + 273.15.\nFinal: {\"answer\": 248.15, \"unit\": \"K\"}", "dedupe_signature": "49cdff87009d4f661480bebaad5f1523570d9ca4cf276ba7fbdda30584842e72", "difficulty": "easy", "final_answer": {"answer": 248.15, "unit": "K"}, "id": "unit_convert_002712_c_to_k_-25", "license": "Apache-2.0", "prompt": "Convert -25 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 -25.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": -25.0}, "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 weighted_sum_002716(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_002716\"}", "dedupe_signature": "e473eaf20563f115ea0bdb73d212cad1699db532b1bcf8353262d50fa8523fe8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_002716"}, "id": "code_002716_weighted_sum_002716", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_002716(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": "validation", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_002716"}, "verifier": {"function": "weighted_sum_002716", "tests": ["assert weighted_sum_002716([2, 3], [4, 5]) == 23", "assert weighted_sum_002716([], []) == 0", "try:\n    weighted_sum_002716([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1155 * 3.16 * 5.\nFinal: {\"answer\": 18249.0, \"unit\": \"J\"}", "dedupe_signature": "63fa6fb3d218724eaaf8782a030f94f4b4c5067b909dcb6a301251a299500c1b", "difficulty": "easy", "final_answer": {"answer": 18249.0, "unit": "J"}, "id": "heat_q_002722_1155_3.16_5", "license": "Apache-2.0", "prompt": "A 1155 g sample has specific heat 3.16 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 = 1155 * 3.16 * 5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 3.16, "mass_g": 1155}, "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 1030 mL to 1.03 L.\n3. Compute M = 0.725 / 1.03.\nFinal: {\"answer\": 0.7039, \"unit\": \"mol/L\"}", "dedupe_signature": "8ddc336014c560dce96f784fa3f7edb3a9114a6cab36edaa8c11fe6c5c880422", "difficulty": "medium", "final_answer": {"answer": 0.7039, "unit": "mol/L"}, "id": "molarity_002726_0.725_1030", "license": "Apache-2.0", "prompt": "A solution contains 0.725 mol of solute in 1030 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1030 mL to 1.03 L.\nCompute M = 0.725 / 1.03.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 0.725, "volume_ml": 1030}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"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\": 0.9981, \"unit\": \"state_units\"}", "dedupe_signature": "2c8620b2681a02a2a6611281dda0811dd08d488cdc4c12479bf42b339bd8a2b0", "difficulty": "medium", "final_answer": {"answer": 0.9981, "unit": "state_units"}, "id": "euler_decay_002745_24_0.41_0.8_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=24, step size h=0.8, 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 24.0, "rate": 0.41, "step": 0.8, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -4.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "8fdf040d8d7d2f19be434803c240a8ab2c502c177bc896d8381033ff451bfbdb", "difficulty": "medium", "final_answer": {"answer": [4.0, -4.75], "unit": "dimensionless"}, "id": "line_two_point_002750_6.25_8.75_4_-4.75", "license": "Apache-2.0", "prompt": "A line passes through points (6.25, 20.25) and (8.75, 30.25). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 6.25, "x2": 8.75, "y1": 20.25, "y2": 30.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "52823e64dfbeebf86c2f428d72438bd3f8cf3b95dadaf7ade4a6690c034cca43", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_002753_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 48.3 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": "validation", "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. 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": "d9676baf9aae82994b086f28c2acf75d162c5775e30ea566a693b2a594d15383", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002769_inconsistent_56040f5d_638988", "license": "Apache-2.0", "prompt": "In model card equation case 638988, 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": "validation", "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_002770(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_002770\"}", "dedupe_signature": "bf2056dcf024f4877fb41307c466c1749b3cb9a8716357f9e1db1ec0e2d63016", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_002770"}, "id": "code_002770_pairwise_ratios_002770", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_002770(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": "validation", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_002770"}, "verifier": {"function": "pairwise_ratios_002770", "tests": ["assert pairwise_ratios_002770([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_002770([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_002770([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_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\": [83.956, -431.916], \"unit\": \"N\"}", "dedupe_signature": "6d169349416c5cf8d2887aaa43eb66bf34abdc3215838d3125aef5d2867406ce", "difficulty": "medium", "final_answer": {"answer": [83.956, -431.916], "unit": "N"}, "id": "vector_components_002785_440_281", "license": "Apache-2.0", "prompt": "A vector has magnitude 440 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 281, "magnitude": 440.0}, "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": "d8cafe2ca2d038dc00cdafa4a5ea564529e7f546d78e0031907523bac2ff1fa5", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002787_consistent_5ca82cb9_77979", "license": "Apache-2.0", "prompt": "In instrument manual case 77979, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "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=21 degrees through the sine of 2 theta.\n3. Substitute v=40.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 110.7776, \"unit\": \"m\"}", "dedupe_signature": "f9fd6cac4aab2f99f252e91b901b9cecb1801ee5385b7e4bd7031989b85061ee", "difficulty": "medium", "final_answer": {"answer": 110.7776, "unit": "m"}, "id": "projectile_range_002792_40.3_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.3 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=40.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=169.1 V and R=126.7 ohm.\nFinal: {\"answer\": 225.6891, \"unit\": \"W\"}", "dedupe_signature": "8ec84d6bffe8207a17b2ffd18fdd6b48781abee76c50a5b73c38b6ac0ea074d4", "difficulty": "easy", "final_answer": {"answer": 225.6891, "unit": "W"}, "id": "ohm_power_002795_169.1_126.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 126.7 ohm and voltage 169.1 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=169.1 V and R=126.7 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 126.7, "voltage": 169.1}, "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 = 2.33 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 102.5433, \"unit\": \"g\"}", "dedupe_signature": "604269a320d2ddee00f4a7b66e5908165ecaf8d93b5a315598fdfa3a3bb51f62", "difficulty": "medium", "final_answer": {"answer": 102.5433, "unit": "g"}, "id": "stoich_mass_002797_carbon_dioxide_2.33", "license": "Apache-2.0", "prompt": "A sample contains 2.33 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 = 2.33 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.33}, "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) = -0.25 y, so each step multiplies y by 1 - h*0.25.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.6503, \"unit\": \"state_units\"}", "dedupe_signature": "a627f8d5940ff76b429c9d5c1893cd7d289611545c5854487cb84d5a84ad99da", "difficulty": "medium", "final_answer": {"answer": 0.6503, "unit": "state_units"}, "id": "euler_decay_002799_71.5_0.25_1.5_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.25 y with y(0)=71.5, 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) = -0.25 y, so each step multiplies y by 1 - h*0.25.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 71.5, "rate": 0.25, "step": 1.5, "steps": 10}, "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 4415.0 / 100.\nFinal: {\"answer\": 44.15, \"unit\": \"m\"}", "dedupe_signature": "2527af873cffbf05267e71e0188ecd50a715a527ffd2727e6a98a491b834c6eb", "difficulty": "easy", "final_answer": {"answer": 44.15, "unit": "m"}, "id": "unit_convert_002802_cm_to_m_4415", "license": "Apache-2.0", "prompt": "Convert 4415 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 4415.0 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 4415.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=89.6 V and R=160.9 ohm.\nFinal: {\"answer\": 49.8953, \"unit\": \"W\"}", "dedupe_signature": "68f8009b15d41e1b52040389ea225b7f4153ad7e347239afd6f33a57533bb85c", "difficulty": "easy", "final_answer": {"answer": 49.8953, "unit": "W"}, "id": "ohm_power_002813_89.6_160.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 160.9 ohm and voltage 89.6 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=89.6 V and R=160.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 160.9, "voltage": 89.6}, "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) = -0.14 y, so each step multiplies y by 1 - h*0.14.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 72.6136, \"unit\": \"state_units\"}", "dedupe_signature": "61acbf21f18d605b8fe0477216fbb843adc2a3fc49cbab542f992aa783af29ed", "difficulty": "medium", "final_answer": {"answer": 72.6136, "unit": "state_units"}, "id": "euler_decay_002817_79_0.14_0.05_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.14 y with y(0)=79, 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) = -0.14 y, so each step multiplies y by 1 - h*0.14.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 79.0, "rate": 0.14, "step": 0.05, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_002842(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_002842\"}", "dedupe_signature": "b7252d7f57b1c14ce6f528e428dc1e7a919c83171b5858c85030c2e1bed1a4c7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_002842"}, "id": "code_002842_safe_mean_002842", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_002842(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": "validation", "task_family": "python_code_generation", "variables": {"function": "safe_mean_002842"}, "verifier": {"function": "safe_mean_002842", "tests": ["assert safe_mean_002842([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_002842(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_002842([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"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)=12.18 and f(-0.8)=9.82.\n3. The interval width is 5.9.\nFinal: {\"answer\": 64.9, \"unit\": \"area_units\"}", "dedupe_signature": "7c18b2deb920c7fc8f51d107ede757708c82a0eb1276df9ec7fbfb53352cfe14", "difficulty": "medium", "final_answer": {"answer": 64.9, "unit": "area_units"}, "id": "trapz_linear_002854_-0.4_9.5_-6.7_-0.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+9.5 from x=-6.7 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(-6.7)=12.18 and f(-0.8)=9.82.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 9.5, "slope": -0.4, "x0": -6.7, "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. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.8, 6.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "60c1d71adc91f89bed1cad01160cdb68d40812989fc019d1eb162f7c8e74d3bc", "difficulty": "medium", "final_answer": {"answer": [2.8, 6.75], "unit": "dimensionless"}, "id": "line_two_point_002858_-11_-4.5_2.8_6.75", "license": "Apache-2.0", "prompt": "A line passes through points (-11, -24.05) and (-4.5, -5.85). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -11.0, "x2": -4.5, "y1": -24.049999999999997, "y2": -5.85}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.7 * 8.314 * 464 / 72.9.\nFinal: {\"answer\": 248.7129, \"unit\": \"kPa\"}", "dedupe_signature": "a26f0b0f347083dee9fe3869cae3e68ee2b68cfb9377e8b1c8273143df20d1a8", "difficulty": "medium", "final_answer": {"answer": 248.7129, "unit": "kPa"}, "id": "ideal_gas_002865_4.7_464_72.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.7 mol, T=464 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 = 4.7 * 8.314 * 464 / 72.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.7, "temp_k": 464, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=356.5 mg, t=126.5 h, and T_half=99 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 147.0314, \"unit\": \"mg\"}", "dedupe_signature": "4e065fbb2b3535a694a4b8f2cee2560efba7e86737aea431bcfc13cdfe3d0ebb", "difficulty": "medium", "final_answer": {"answer": 147.0314, "unit": "mg"}, "id": "half_life_002868_356.5_99_126.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 356.5 mg. Its half-life is 99 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=356.5 mg, t=126.5 h, and T_half=99 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 126.5, "half_life": 99.0, "initial_amount": 356.5}, "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 = 1.91 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 191.1662, \"unit\": \"g\"}", "dedupe_signature": "e5faa15ec6ef5e890ad16ad6b76df3b9c27fb3cf12d96a939d932c39039e5fad", "difficulty": "medium", "final_answer": {"answer": 191.1662, "unit": "g"}, "id": "stoich_mass_002869_calcium_carbonate_1.91", "license": "Apache-2.0", "prompt": "A sample contains 1.91 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 = 1.91 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.91}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -20.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "2d1ccb8aedba565845b57b7f02244a8929f1140fd6ab191f48e3a222d023fe2b", "difficulty": "medium", "final_answer": {"answer": [9.45, -20.0], "unit": "dimensionless"}, "id": "line_two_point_002876_6.75_10.25_9.45_-20", "license": "Apache-2.0", "prompt": "A line passes through points (6.75, 43.7875) and (10.25, 76.8625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "linear_modeling", "variables": {"x1": 6.75, "x2": 10.25, "y1": 43.787499999999994, "y2": 76.8625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 85 * 0.615 * 57.\nFinal: {\"answer\": 2979.675, \"unit\": \"J\"}", "dedupe_signature": "4fb9090fa58b7e386bc8066b6dd94d2fcee095d89006ef336f12cbd577175e01", "difficulty": "easy", "final_answer": {"answer": 2979.675, "unit": "J"}, "id": "heat_q_002884_85_0.615_57", "license": "Apache-2.0", "prompt": "A 85 g sample has specific heat 0.615 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 = 85 * 0.615 * 57.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 57, "heat_capacity": 0.615, "mass_g": 85}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"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 6 steps and round the final state.\nFinal: {\"answer\": 0.2898, \"unit\": \"state_units\"}", "dedupe_signature": "aa1dfd2024e1a90441f821ed3d9aaed11e3623a9c3ae33cd1facc25c047e5a58", "difficulty": "medium", "final_answer": {"answer": 0.2898, "unit": "state_units"}, "id": "euler_decay_002889_1_0.93_1.95_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.93 y with y(0)=1, 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) = -0.93 y, so each step multiplies y by 1 - h*0.93.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 1.0, "rate": 0.93, "step": 1.95, "steps": 6}, "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 115.0 + 273.15.\nFinal: {\"answer\": 388.15, \"unit\": \"K\"}", "dedupe_signature": "42bd4685814d15c257f47dbc47946ebabb821ea2c5c7dfe68a8096436d67025a", "difficulty": "easy", "final_answer": {"answer": 388.15, "unit": "K"}, "id": "unit_convert_002892_c_to_k_115", "license": "Apache-2.0", "prompt": "Convert 115 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 115.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 115.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24.55^2 and multiply by 0.5 * 16.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4987.3632, \"unit\": \"J\"}", "dedupe_signature": "3c006a132cf1b12fb4a6301d7bdbe8a9de371e83802ff01d06727049bbacc3c1", "difficulty": "easy", "final_answer": {"answer": 4987.3632, "unit": "J"}, "id": "ke_002917_16.55_24.55", "license": "Apache-2.0", "prompt": "A body of mass 16.55 kg moves at 24.55 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 = 24.55^2 and multiply by 0.5 * 16.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.55, "velocity": 24.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.312, 1.081, 0.454], \"unit\": \"temperature_units\"}", "dedupe_signature": "e92d0e93d497b210d7e3db5f50dc4b8ffefa8b144ae66df87779be8597dd6c68", "difficulty": "hard", "final_answer": {"answer": [1.312, 1.081, 0.454], "unit": "temperature_units"}, "id": "heat_step_002927_0.42_1.3_-0.2_1.9_2.05_-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=1.3, right=-1.6; current interior values are [-0.2, 1.9, 2.05]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, 1.9, 2.05], "left": 1.3, "r": 0.42, "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=121 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-222.754, 370.7249], \"unit\": \"N\"}", "dedupe_signature": "eec20bde3e76f182baa1a078fa02b58c87fc7410d51c5b70bcb8bfdb90c6f587", "difficulty": "medium", "final_answer": {"answer": [-222.754, 370.7249], "unit": "N"}, "id": "vector_components_002929_432.5_121", "license": "Apache-2.0", "prompt": "A vector has magnitude 432.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 121, "magnitude": 432.5}, "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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.3)=-33.4 and f(16)=-48.8.\n3. The interval width is 7.7.\nFinal: {\"answer\": -316.47, \"unit\": \"area_units\"}", "dedupe_signature": "c5a9b1ffabed0841ce994bf518b9530b0bb337bc28d643e8da6a4d0d58a8f92a", "difficulty": "medium", "final_answer": {"answer": -316.47, "unit": "area_units"}, "id": "trapz_linear_002944_-2_-16.8_8.3_16", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2x+-16.8 from x=8.3 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(8.3)=-33.4 and f(16)=-48.8.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -16.8, "slope": -2.0, "x0": 8.3, "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4290 mL to 4.29 L.\n3. Compute M = 4.18 / 4.29.\nFinal: {\"answer\": 0.9744, \"unit\": \"mol/L\"}", "dedupe_signature": "36000f42684eea5f9afc514b4d901c0e1d066dd61845bc9a90fe9aac4e81a188", "difficulty": "medium", "final_answer": {"answer": 0.9744, "unit": "mol/L"}, "id": "molarity_002978_4.18_4290", "license": "Apache-2.0", "prompt": "A solution contains 4.18 mol of solute in 4290 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4290 mL to 4.29 L.\nCompute M = 4.18 / 4.29.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.18, "volume_ml": 4290}, "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=0.28 and add it to the current value.\nFinal: {\"answer\": [-0.866, -0.292, 1.74], \"unit\": \"temperature_units\"}", "dedupe_signature": "4e8baef2436467e0005967892827d759a9eb3a92bf7ef3049ddd4588d016d2cc", "difficulty": "hard", "final_answer": {"answer": [-0.866, -0.292, 1.74], "unit": "temperature_units"}, "id": "heat_step_002981_0.28_1.35_-2.0_-1.3_3.0_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=1.35, right=2.8; current interior values are [-2.0, -1.3, 3.0]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-2.0, -1.3, 3.0], "left": 1.35, "r": 0.28, "right": 2.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"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": "7c7087ff15c2599318b9fb6d0dd5983cebf27904c8d2188b84a8e1dc8ad4a81f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002985_inconsistent_74ac0b02_113615", "license": "Apache-2.0", "prompt": "In simulation spec case 113615, 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": "validation", "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_003040(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_003040\"}", "dedupe_signature": "4d8555267aee3d6e1746175e0d47dfda6fbcf44d871ce653e3c78f8265579f45", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_003040"}, "id": "code_003040_running_total_003040", "license": "Apache-2.0", "prompt": "Write a Python function running_total_003040(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_003040"}, "verifier": {"function": "running_total_003040", "tests": ["assert running_total_003040([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_003040(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_003040([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.15^2 and multiply by 0.5 * 0.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 70.1207, \"unit\": \"J\"}", "dedupe_signature": "846d39ac33f16743ed8f892e612b793ccb677c633bbe3f195037b72f5cc9feb6", "difficulty": "easy", "final_answer": {"answer": 70.1207, "unit": "J"}, "id": "ke_003043_0.95_12.15", "license": "Apache-2.0", "prompt": "A body of mass 0.95 kg moves at 12.15 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 = 12.15^2 and multiply by 0.5 * 0.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.95, "velocity": 12.15}, "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=37 degrees through the sine of 2 theta.\n3. Substitute v=69.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 467.8738, \"unit\": \"m\"}", "dedupe_signature": "93e774d504765f0a9eabad987609b7c68e81d12539e846a3cf48a546ff7d7ff4", "difficulty": "medium", "final_answer": {"answer": 467.8738, "unit": "m"}, "id": "projectile_range_003044_69.1_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 69.1 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=69.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 69.1}, "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 = 0.8 * 8.314 * 387 / 118.3.\nFinal: {\"answer\": 21.7584, \"unit\": \"kPa\"}", "dedupe_signature": "03671b3518a8e6c45dcb47f07d5aeb755b4059849588fc0813166c3c8e8ac74b", "difficulty": "medium", "final_answer": {"answer": 21.7584, "unit": "kPa"}, "id": "ideal_gas_003063_0.8_387_118.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.8 mol, T=387 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 = 0.8 * 8.314 * 387 / 118.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.8, "temp_k": 387, "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. Mass equals amount in moles times molar mass.\n2. Use m = 0.95 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 171.1482, \"unit\": \"g\"}", "dedupe_signature": "6687be5038db8bbe8a0c5d467403243a6876d273b6b407b8980dee4e8d874cc1", "difficulty": "medium", "final_answer": {"answer": 171.1482, "unit": "g"}, "id": "stoich_mass_003067_glucose_0.95", "license": "Apache-2.0", "prompt": "A sample contains 0.95 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 = 0.95 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.95}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [-44.7442, -318.3712], \"unit\": \"N\"}", "dedupe_signature": "10eb500c29660b329005a8f5e2e80f0544fa3bc66d47c725dada488e8244c10f", "difficulty": "medium", "final_answer": {"answer": [-44.7442, -318.3712], "unit": "N"}, "id": "vector_components_003073_321.5_262", "license": "Apache-2.0", "prompt": "A vector has magnitude 321.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 262, "magnitude": 321.5}, "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. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 75 * 3.92 * 5.\nFinal: {\"answer\": 1470.0, \"unit\": \"J\"}", "dedupe_signature": "0e973428ef1a3ce17d7c891dd19e58f34dcb3d307a041c413b6656107b9241bc", "difficulty": "easy", "final_answer": {"answer": 1470.0, "unit": "J"}, "id": "heat_q_003082_75_3.92_5", "license": "Apache-2.0", "prompt": "A 75 g sample has specific heat 3.92 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 = 75 * 3.92 * 5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 3.92, "mass_g": 75}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.05^2 and multiply by 0.5 * 10.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2160.7634, \"unit\": \"J\"}", "dedupe_signature": "4fdf28574fa1eadb75598b5f7329a6313349bdbbdd33a421dbd0acee026e12df", "difficulty": "easy", "final_answer": {"answer": 2160.7634, "unit": "J"}, "id": "ke_003097_10.75_20.05", "license": "Apache-2.0", "prompt": "A body of mass 10.75 kg moves at 20.05 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 = 20.05^2 and multiply by 0.5 * 10.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.75, "velocity": 20.05}, "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 = 2.98 * 8.314 * 326 / 10.8.\nFinal: {\"answer\": 747.8597, \"unit\": \"kPa\"}", "dedupe_signature": "2733fce4bf7a6df24d1c49c14678cf55bbc59d8a0c81f87ea8e5b3ca6d838a9e", "difficulty": "medium", "final_answer": {"answer": 747.8597, "unit": "kPa"}, "id": "ideal_gas_003099_2.98_326_10.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.98 mol, T=326 K, and V=10.8 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 = 2.98 * 8.314 * 326 / 10.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.98, "temp_k": 326, "volume_l": 10.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.47, 1.67, 2.08], \"unit\": \"temperature_units\"}", "dedupe_signature": "913c55b09475b97a2985d26acd42dce60af193e6d3125d2efeb916e085bdea5a", "difficulty": "hard", "final_answer": {"answer": [-0.47, 1.67, 2.08], "unit": "temperature_units"}, "id": "heat_step_003107_0.2_-0.75_-1.4_2.6_1.95_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=-0.75, right=1.95; current interior values are [-1.4, 2.6, 1.95]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, 2.6, 1.95], "left": -0.75, "r": 0.2, "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 12611.0 / 1000.\nFinal: {\"answer\": 12.611, \"unit\": \"kg\"}", "dedupe_signature": "909901fea721473249ddf8b0d3ddc3bcb904b0aef620f2c765988dd1dcf0d5d7", "difficulty": "easy", "final_answer": {"answer": 12.611, "unit": "kg"}, "id": "unit_convert_003108_g_to_kg_12611", "license": "Apache-2.0", "prompt": "Convert 12611 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 12611.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 12611.0}, "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=3 degrees and keep the unit as newtons.\nFinal: {\"answer\": [275.6218, 14.4447], \"unit\": \"N\"}", "dedupe_signature": "0d5e8f44740690efec1aa91b147cbfefb87ddeaa3b3641afc68f4a94d4608472", "difficulty": "medium", "final_answer": {"answer": [275.6218, 14.4447], "unit": "N"}, "id": "vector_components_003109_276_3", "license": "Apache-2.0", "prompt": "A vector has magnitude 276 N at 3 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=3 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 3, "magnitude": 276.0}, "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. Use the ideal gas law P V = n R 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 * 254 / 4.3.\nFinal: {\"answer\": 2499.7298, \"unit\": \"kPa\"}", "dedupe_signature": "54695909e5dfb0d930763aae698756d220407dfe05514277813022f97c93a9f0", "difficulty": "medium", "final_answer": {"answer": 2499.7298, "unit": "kPa"}, "id": "ideal_gas_003117_5.09_254_4.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.09 mol, T=254 K, and V=4.3 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 = 5.09 * 8.314 * 254 / 4.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 5.09, "temp_k": 254, "volume_l": 4.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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": "a460d53b890340e96ec2f4bc6235db3b085eb2b21cdd1376cfc822f8d0449645", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003131_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 [-1.95, -1.5, -1.55], 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": "validation", "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=114.9 V and R=81.8 ohm.\nFinal: {\"answer\": 161.3938, \"unit\": \"W\"}", "dedupe_signature": "25380e0a7acc87afbe6d3492c983c1334be0888a4506af46f44861c3796b0f7d", "difficulty": "easy", "final_answer": {"answer": 161.3938, "unit": "W"}, "id": "ohm_power_003137_114.9_81.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 81.8 ohm and voltage 114.9 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=114.9 V and R=81.8 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 81.8, "voltage": 114.9}, "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(6.1)=-54.03 and f(9.8)=-77.34.\n3. The interval width is 3.7.\nFinal: {\"answer\": -243.0345, \"unit\": \"area_units\"}", "dedupe_signature": "611a68431e3cf36c441cb3f1a1b98fca4d721381d5a5992e3a26d78a569f6d7d", "difficulty": "medium", "final_answer": {"answer": -243.0345, "unit": "area_units"}, "id": "trapz_linear_003160_-6.3_-15.6_6.1_9.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.3x+-15.6 from x=6.1 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(6.1)=-54.03 and f(9.8)=-77.34.\nThe interval width is 3.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -15.6, "slope": -6.3, "x0": 6.1, "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\": [0.78, 0.534, 0.14], \"unit\": \"temperature_units\"}", "dedupe_signature": "710cf5fcae0bd9baada8915f51de8388ced721a8698ef9f4e6f7553cb692c2b0", "difficulty": "hard", "final_answer": {"answer": [0.78, 0.534, 0.14], "unit": "temperature_units"}, "id": "heat_step_003161_0.32_-0.2_1.5_0.95_-0.9_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=-0.2, right=0.5; current interior values are [1.5, 0.95, -0.9]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, 0.95, -0.9], "left": -0.2, "r": 0.32, "right": 0.5}, "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": "ddee28bd98d3737a3ea4b343c23e136b4138f85f96cce4361c1a2162944bfd3a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003165_inconsistent_7481c798_393800", "license": "Apache-2.0", "prompt": "In sensor calibration case 393800, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"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 25573.0 / 1000.\nFinal: {\"answer\": 25.573, \"unit\": \"kg\"}", "dedupe_signature": "f883c8e684c042ddb4bdbd93bf12de57b76f482304647b0d426c7a9cac5ec2e5", "difficulty": "easy", "final_answer": {"answer": 25.573, "unit": "kg"}, "id": "unit_convert_003180_g_to_kg_25573", "license": "Apache-2.0", "prompt": "Convert 25573 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 25573.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 25573.0}, "verifier": {"formula": "value / 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)=-12.7 and f(10.6)=-15.12.\n3. The interval width is 1.1.\nFinal: {\"answer\": -15.301, \"unit\": \"area_units\"}", "dedupe_signature": "f2f561b145acca7a2e38c9dab16576f66f33bd3e54bbb07f7a6cc84ec2cae3ef", "difficulty": "medium", "final_answer": {"answer": -15.301, "unit": "area_units"}, "id": "trapz_linear_003196_-2.2_8.2_9.5_10.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+8.2 from x=9.5 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(9.5)=-12.7 and f(10.6)=-15.12.\nThe interval width is 1.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 8.2, "slope": -2.2, "x0": 9.5, "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. 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\": [7.5, -12.9904], \"unit\": \"N\"}", "dedupe_signature": "86e56c850e33eb29b9e931f5a939a22cb6d7f29a2d34dcd0e4f9b1001a7036d1", "difficulty": "medium", "final_answer": {"answer": [7.5, -12.9904], "unit": "N"}, "id": "vector_components_003199_15_300", "license": "Apache-2.0", "prompt": "A vector has magnitude 15 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 300, "magnitude": 15.0}, "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: 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": "25f61475e28e447f2dc476dead855e1808d34e43ba4f13b6ed315d9473fadc8f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003221_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 [1.45, 0.35, -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": "validation", "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3205 mL to 3.205 L.\n3. Compute M = 4.96 / 3.205.\nFinal: {\"answer\": 1.5476, \"unit\": \"mol/L\"}", "dedupe_signature": "f8de933457448d9dfce85daf2a4ec20a636b3355f07d89ee5c5711e4d56f8410", "difficulty": "medium", "final_answer": {"answer": 1.5476, "unit": "mol/L"}, "id": "molarity_003230_4.96_3205", "license": "Apache-2.0", "prompt": "A solution contains 4.96 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 = 4.96 / 3.205.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.96, "volume_ml": 3205}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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 * 2.355 * 29.\nFinal: {\"answer\": 8878.35, \"unit\": \"J\"}", "dedupe_signature": "25a4981786c42a739d09d4b60821e5c0442d12549a98e36ccddaf0c3ad174446", "difficulty": "easy", "final_answer": {"answer": 8878.35, "unit": "J"}, "id": "heat_q_003244_130_2.355_29", "license": "Apache-2.0", "prompt": "A 130 g sample has specific heat 2.355 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 = 130 * 2.355 * 29.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 29, "heat_capacity": 2.355, "mass_g": 130}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 13.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "ba8cc392db7133416f71a14354dce25eec3172ccec24a1259a03cec2f24040f6", "difficulty": "medium", "final_answer": {"answer": [8.0, 13.0], "unit": "dimensionless"}, "id": "line_two_point_003254_-12.5_-9.25_8_13", "license": "Apache-2.0", "prompt": "A line passes through points (-12.5, -87) and (-9.25, -61). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "linear_modeling", "variables": {"x1": -12.5, "x2": -9.25, "y1": -87.0, "y2": -61.0}, "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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.5)=31.25 and f(7.3)=-16.77.\n3. The interval width is 9.8.\nFinal: {\"answer\": 70.952, \"unit\": \"area_units\"}", "dedupe_signature": "ed45bb9eda62999504ad8396c792965e18d1b8ff267270e2f46e625dfb922fee", "difficulty": "medium", "final_answer": {"answer": 70.952, "unit": "area_units"}, "id": "trapz_linear_003286_-4.9_19_-2.5_7.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+19 from x=-2.5 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(-2.5)=31.25 and f(7.3)=-16.77.\nThe interval width is 9.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 19.0, "slope": -4.9, "x0": -2.5, "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. 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": "057c2e49d6ef3e5058c7923afff1865309896b0d2579f039c7be74c03b746d8c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_003293_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry crop record from batch 582924 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": "validation", "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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.2)=41.46 and f(5.6)=50.28.\n3. The interval width is 1.4.\nFinal: {\"answer\": 64.218, \"unit\": \"area_units\"}", "dedupe_signature": "15c1cb341f14461e2b9f651dfc67be691729edc5ea43c63660cabec7be3879c5", "difficulty": "medium", "final_answer": {"answer": 64.218, "unit": "area_units"}, "id": "trapz_linear_003304_6.3_15_4.2_5.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+15 from x=4.2 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(4.2)=41.46 and f(5.6)=50.28.\nThe interval width is 1.4.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 15.0, "slope": 6.3, "x0": 4.2, "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. 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": "b607cecc26f81b8403c57f08db6b061cef032fccbe8446af87189fe7e617ac1b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003309_inconsistent_1e14b074_4877", "license": "Apache-2.0", "prompt": "In simulation spec case 4877, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "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 = 5.96 * 8.314 * 482 / 91.7.\nFinal: {\"answer\": 260.4558, \"unit\": \"kPa\"}", "dedupe_signature": "d168538e433c47887ca090826d9ac0d4840b6d5caba715ec934e9125dbd89004", "difficulty": "medium", "final_answer": {"answer": 260.4558, "unit": "kPa"}, "id": "ideal_gas_003315_5.96_482_91.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.96 mol, T=482 K, and V=91.7 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 = 5.96 * 8.314 * 482 / 91.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 5.96, "temp_k": 482, "volume_l": 91.7}, "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=99.7 V and R=27.1 ohm.\nFinal: {\"answer\": 366.793, \"unit\": \"W\"}", "dedupe_signature": "08f84cd4c8db23e57dc2a64bb4e20f65f2acd918c53db30fff32a568c5e89a89", "difficulty": "easy", "final_answer": {"answer": 366.793, "unit": "W"}, "id": "ohm_power_003335_99.7_27.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 27.1 ohm and voltage 99.7 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=99.7 V and R=27.1 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 27.1, "voltage": 99.7}, "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) = -0.15 y, so each step multiplies y by 1 - h*0.15.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 15.0591, \"unit\": \"state_units\"}", "dedupe_signature": "19ff53dc1ef37a1c6aa83249b4457f3d330895745faa97d94718f35982f1cbe4", "difficulty": "medium", "final_answer": {"answer": 15.0591, "unit": "state_units"}, "id": "euler_decay_003339_16.5_0.15_0.2_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=16.5, step size h=0.2, 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) = -0.15 y, so each step multiplies y by 1 - h*0.15.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 16.5, "rate": 0.15, "step": 0.2, "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=0.24 and add it to the current value.\nFinal: {\"answer\": [-0.336, -0.084, 1.348], \"unit\": \"temperature_units\"}", "dedupe_signature": "572b026615e23d3d17c1571a68194739babc350a17c4aa12e9b3189270e3475b", "difficulty": "hard", "final_answer": {"answer": [-0.336, -0.084, 1.348], "unit": "temperature_units"}, "id": "heat_step_003341_0.24_0.15_-0.3_-0.9_1.9_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=0.15, right=2.4; current interior values are [-0.3, -0.9, 1.9]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.3, -0.9, 1.9], "left": 0.15, "r": 0.24, "right": 2.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"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": "ca7e440839a04e1cc2f955d53e377c3edc51be8ce795a61466e961f9bc9367eb", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003345_consistent_741d4e34_185920", "license": "Apache-2.0", "prompt": "In model card equation case 185920, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "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=34 degrees through the sine of 2 theta.\n3. Substitute v=60.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 343.662, \"unit\": \"m\"}", "dedupe_signature": "f15e3269aa848f526854fdc8d91724c212e2a91829d306254f86e19e0b948d39", "difficulty": "medium", "final_answer": {"answer": 343.662, "unit": "m"}, "id": "projectile_range_003368_60.3_34", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.3 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=60.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 34, "gravity": 9.81, "speed": 60.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3330 mL to 3.33 L.\n3. Compute M = 4.665 / 3.33.\nFinal: {\"answer\": 1.4009, \"unit\": \"mol/L\"}", "dedupe_signature": "1f746f6f55d79238a5cbcb2230b7aa95e60868c9a27939462f32f3dbc6d49e89", "difficulty": "medium", "final_answer": {"answer": 1.4009, "unit": "mol/L"}, "id": "molarity_003374_4.665_3330", "license": "Apache-2.0", "prompt": "A solution contains 4.665 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 = 4.665 / 3.33.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.665, "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) = -0.47 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\": 1.0697, \"unit\": \"state_units\"}", "dedupe_signature": "70c08453af7f9dcf1c0c6f03990a33f19e2ce162212393450c0df5052d311047", "difficulty": "medium", "final_answer": {"answer": 1.0697, "unit": "state_units"}, "id": "euler_decay_003375_59_0.47_0.65_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.47 y with y(0)=59, 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) = -0.47 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 59.0, "rate": 0.47, "step": 0.65, "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(5.6)=-10.94 and f(7.4)=-8.96.\n3. The interval width is 1.8.\nFinal: {\"answer\": -17.91, \"unit\": \"area_units\"}", "dedupe_signature": "416ee63b87ec98bf6d31f16e6ab6ac2bf9a55071d1068699f499edb2c723993d", "difficulty": "medium", "final_answer": {"answer": -17.91, "unit": "area_units"}, "id": "trapz_linear_003394_1.1_-17.1_5.6_7.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.1x+-17.1 from x=5.6 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(5.6)=-10.94 and f(7.4)=-8.96.\nThe interval width is 1.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -17.1, "slope": 1.1, "x0": 5.6, "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. Use Newton's second law F = m a.\n2. Substitute m = 5.55 kg and a = 4.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 22.4775, \"unit\": \"N\"}", "dedupe_signature": "0758b455599b5f1cdee5861142fb34ecf2f49f102021458d11c7a1786b73af35", "difficulty": "easy", "final_answer": {"answer": 22.4775, "unit": "N"}, "id": "force_003402_5.55_4.05", "license": "Apache-2.0", "prompt": "A cart has mass 5.55 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 = 5.55 kg and a = 4.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.05, "mass": 5.55}, "verifier": {"formula": "mass * acceleration", "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)=43.86 and f(-1.9)=17.94.\n3. The interval width is 7.2.\nFinal: {\"answer\": 222.48, \"unit\": \"area_units\"}", "dedupe_signature": "81b7cd6ee7f2a6baa31df03367f54ca58f89337adfd373a419765b08acd8caa8", "difficulty": "medium", "final_answer": {"answer": 222.48, "unit": "area_units"}, "id": "trapz_linear_003412_-3.6_11.1_-9.1_-1.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+11.1 from x=-9.1 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(-9.1)=43.86 and f(-1.9)=17.94.\nThe interval width is 7.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 11.1, "slope": -3.6, "x0": -9.1, "x1": -1.8999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 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 = 0.57 * 8.314 * 379 / 73.6.\nFinal: {\"answer\": 24.4032, \"unit\": \"kPa\"}", "dedupe_signature": "11e012df4c294e46d9ca489dc4f43969eba0fcff4990355eef08c263de6372fc", "difficulty": "medium", "final_answer": {"answer": 24.4032, "unit": "kPa"}, "id": "ideal_gas_003423_0.57_379_73.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.57 mol, T=379 K, and V=73.6 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 = 0.57 * 8.314 * 379 / 73.6.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.57, "temp_k": 379, "volume_l": 73.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1005 mL to 1.005 L.\n3. Compute M = 2.34 / 1.005.\nFinal: {\"answer\": 2.3284, \"unit\": \"mol/L\"}", "dedupe_signature": "e3b8dd6f57c494b98c6e089fb7b2052cbeec51d6302b2788808ec3a291d66730", "difficulty": "medium", "final_answer": {"answer": 2.3284, "unit": "mol/L"}, "id": "molarity_003428_2.34_1005", "license": "Apache-2.0", "prompt": "A solution contains 2.34 mol of solute in 1005 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1005 mL to 1.005 L.\nCompute M = 2.34 / 1.005.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.34, "volume_ml": 1005}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=104.6 V and R=9.5 ohm.\nFinal: {\"answer\": 1151.7011, \"unit\": \"W\"}", "dedupe_signature": "fabbcf634e95cf6b87acca61ea0bbfa032924bfa42fc0874e0a2d7bbd3e97de3", "difficulty": "easy", "final_answer": {"answer": 1151.7011, "unit": "W"}, "id": "ohm_power_003461_104.6_9.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 9.5 ohm and voltage 104.6 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=104.6 V and R=9.5 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 9.5, "voltage": 104.6}, "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(5.3)=-24.07 and f(11.2)=-70.68.\n3. The interval width is 5.9.\nFinal: {\"answer\": -279.5125, \"unit\": \"area_units\"}", "dedupe_signature": "7918feb216ba1b8fbda05522c0f7f90ced0a6dc7d70cf1eb735f13da1ff2d239", "difficulty": "medium", "final_answer": {"answer": -279.5125, "unit": "area_units"}, "id": "trapz_linear_003466_-7.9_17.8_5.3_11.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.9x+17.8 from x=5.3 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(5.3)=-24.07 and f(11.2)=-70.68.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 17.8, "slope": -7.9, "x0": 5.3, "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. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1896.0 / 100.\nFinal: {\"answer\": 18.96, \"unit\": \"m\"}", "dedupe_signature": "3833f4c5764f49d4888f6371fb05f4634b3d8157543f89d3d3362d3fb74fdc5c", "difficulty": "easy", "final_answer": {"answer": 18.96, "unit": "m"}, "id": "unit_convert_003468_cm_to_m_1896", "license": "Apache-2.0", "prompt": "Convert 1896 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 1896.0 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 1896.0}, "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\": [-2.5, -0.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "e63e90a178199ecb464216cb878d8bcca7b46e4e94b97e6d8f486a372176c09b", "difficulty": "medium", "final_answer": {"answer": [-2.5, -0.25], "unit": "dimensionless"}, "id": "line_two_point_003470_-18.25_-3.25_-2.5_-0.25", "license": "Apache-2.0", "prompt": "A line passes through points (-18.25, 45.375) and (-3.25, 7.875). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -18.25, "x2": -3.25, "y1": 45.375, "y2": 7.875}, "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. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "429402d8cc4bfb70b7f6910632dac1aa50209e906aa388fc2704df75cffead96", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003471_inconsistent_74ac0b02_593012", "license": "Apache-2.0", "prompt": "In student derivation case 593012, 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": "validation", "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_003472(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_003472\"}", "dedupe_signature": "6d9928d3db32edf14cc12126710f863d59c943a27330844921f9ece0285f91b2", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_003472"}, "id": "code_003472_weighted_sum_003472", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_003472(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": "validation", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_003472"}, "verifier": {"function": "weighted_sum_003472", "tests": ["assert weighted_sum_003472([2, 3], [4, 5]) == 23", "assert weighted_sum_003472([], []) == 0", "try:\n    weighted_sum_003472([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"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 mg, t=63.5 h, and T_half=24 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 118.877, \"unit\": \"mg\"}", "dedupe_signature": "2eaafc9957de0b3c3341e5c16653237242bc81d799a57480a4825f1e417bb31b", "difficulty": "medium", "final_answer": {"answer": 118.877, "unit": "mg"}, "id": "half_life_003480_744_24_63.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 744 mg. Its half-life is 24 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=744 mg, t=63.5 h, and T_half=24 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 63.5, "half_life": 24.0, "initial_amount": 744.0}, "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 1315 mL to 1.315 L.\n3. Compute M = 2.73 / 1.315.\nFinal: {\"answer\": 2.076, \"unit\": \"mol/L\"}", "dedupe_signature": "fcec7883fc64353c2e3b16549e0863ab951e6e0cfc4459669faa75d48d566a45", "difficulty": "medium", "final_answer": {"answer": 2.076, "unit": "mol/L"}, "id": "molarity_003482_2.73_1315", "license": "Apache-2.0", "prompt": "A solution contains 2.73 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 = 2.73 / 1.315.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.73, "volume_ml": 1315}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.45^2 and multiply by 0.5 * 26.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 396.5284, \"unit\": \"J\"}", "dedupe_signature": "8b35ceed7096b59e595be1de9a33ca981680b4ce3950b424f0262985351ebaa4", "difficulty": "easy", "final_answer": {"answer": 396.5284, "unit": "J"}, "id": "ke_003493_26.7_5.45", "license": "Apache-2.0", "prompt": "A body of mass 26.7 kg moves at 5.45 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 = 5.45^2 and multiply by 0.5 * 26.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.7, "velocity": 5.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.7 kg and a = 13.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 100.485, \"unit\": \"N\"}", "dedupe_signature": "0f0300f345625ae2ada3f558ddccfc6724473a0ca534378478e0c7db30003c0d", "difficulty": "easy", "final_answer": {"answer": 100.485, "unit": "N"}, "id": "force_003510_7.7_13.05", "license": "Apache-2.0", "prompt": "A cart has mass 7.7 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 = 7.7 kg and a = 13.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.05, "mass": 7.7}, "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 = 1855 * 0.985 * 73.\nFinal: {\"answer\": 133383.775, \"unit\": \"J\"}", "dedupe_signature": "3f3b4de964a052d80a25972f8e5787d21d3d62ccfed3dc6e80c6f66fda48cdf3", "difficulty": "easy", "final_answer": {"answer": 133383.775, "unit": "J"}, "id": "heat_q_003514_1855_0.985_73", "license": "Apache-2.0", "prompt": "A 1855 g sample has specific heat 0.985 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 = 1855 * 0.985 * 73.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 73, "heat_capacity": 0.985, "mass_g": 1855}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 4.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "b67d283afc2c5004af234091518982c6f07aa70ade748355584165635b3e9adb", "difficulty": "medium", "final_answer": {"answer": [8.25, 4.0], "unit": "dimensionless"}, "id": "line_two_point_003524_-6.5_4_8.25_4", "license": "Apache-2.0", "prompt": "A line passes through points (-6.5, -49.625) and (4, 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -6.5, "x2": 4.0, "y1": -49.625, "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. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.85^2 and multiply by 0.5 * 16.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3553.8564, \"unit\": \"J\"}", "dedupe_signature": "b0c36d1f5025db9d7258ac0bf61d8c101a33a55b674a703a89d5d4c81f01ca1d", "difficulty": "easy", "final_answer": {"answer": 3553.8564, "unit": "J"}, "id": "ke_003529_16.35_20.85", "license": "Apache-2.0", "prompt": "A body of mass 16.35 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 * 16.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.35, "velocity": 20.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.68 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 168.1462, \"unit\": \"g\"}", "dedupe_signature": "aace9c031e7d0b593af61b29f0bf9093eed9fa87e17f3429d569442424227d32", "difficulty": "medium", "final_answer": {"answer": 168.1462, "unit": "g"}, "id": "stoich_mass_003535_calcium_carbonate_1.68", "license": "Apache-2.0", "prompt": "A sample contains 1.68 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 = 1.68 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.68}, "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 1295 mL to 1.295 L.\n3. Compute M = 1.225 / 1.295.\nFinal: {\"answer\": 0.9459, \"unit\": \"mol/L\"}", "dedupe_signature": "7b45bcecc0b8ad54c5e912fbd7e5204153870ade04e7e1a4d0f3644f8f3806c5", "difficulty": "medium", "final_answer": {"answer": 0.9459, "unit": "mol/L"}, "id": "molarity_003554_1.225_1295", "license": "Apache-2.0", "prompt": "A solution contains 1.225 mol of solute in 1295 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1295 mL to 1.295 L.\nCompute M = 1.225 / 1.295.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 1.225, "volume_ml": 1295}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.75^2 and multiply by 0.5 * 6.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2367.9422, \"unit\": \"J\"}", "dedupe_signature": "f5d292bebc45af6a2982346fb59ced337c5394014e35ffc6b046e51e85048e4c", "difficulty": "easy", "final_answer": {"answer": 2367.9422, "unit": "J"}, "id": "ke_003565_6.15_27.75", "license": "Apache-2.0", "prompt": "A body of mass 6.15 kg moves at 27.75 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 = 27.75^2 and multiply by 0.5 * 6.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.15, "velocity": 27.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.683, 0.492, -0.669], \"unit\": \"temperature_units\"}", "dedupe_signature": "658dfc7da6525bbbdb018f148739d736c97c91abe0f6e8eb3226331b887880cb", "difficulty": "hard", "final_answer": {"answer": [1.683, 0.492, -0.669], "unit": "temperature_units"}, "id": "heat_step_003575_0.22_2.65_1.65_0.8_-1.45_-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=2.65, right=-0.15; current interior values are [1.65, 0.8, -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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.65, 0.8, -1.45], "left": 2.65, "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 43977.0 / 1000.\nFinal: {\"answer\": 43.977, \"unit\": \"kg\"}", "dedupe_signature": "09fcb76ca864b2c69c1fee91a3fe23b93d4902a0b31336b577c5af913cf39afb", "difficulty": "easy", "final_answer": {"answer": 43.977, "unit": "kg"}, "id": "unit_convert_003576_g_to_kg_43977", "license": "Apache-2.0", "prompt": "Convert 43977 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 43977.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 43977.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 14.45^2 and multiply by 0.5 * 14.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1534.6984, \"unit\": \"J\"}", "dedupe_signature": "250f1c0488894af23bd940222014030a6259e8b3f88644796775b7c2a4d22ec5", "difficulty": "easy", "final_answer": {"answer": 1534.6984, "unit": "J"}, "id": "ke_003583_14.7_14.45", "license": "Apache-2.0", "prompt": "A body of mass 14.7 kg moves at 14.45 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 = 14.45^2 and multiply by 0.5 * 14.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.7, "velocity": 14.45}, "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=41.3 V and R=132.7 ohm.\nFinal: {\"answer\": 12.8537, \"unit\": \"W\"}", "dedupe_signature": "52ca3eb00e9bc9c4b0cf3e5f1b7fc25529f0673fbb3cdcdd2054874be756f687", "difficulty": "easy", "final_answer": {"answer": 12.8537, "unit": "W"}, "id": "ohm_power_003605_41.3_132.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 132.7 ohm and voltage 41.3 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=41.3 V and R=132.7 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 132.7, "voltage": 41.3}, "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) = -0.04 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\": 6.3584, \"unit\": \"state_units\"}", "dedupe_signature": "0555cb1a6a43ec13187b43f7953b46e13823ad0c5626001758ca3ee1adcb1656", "difficulty": "medium", "final_answer": {"answer": 6.3584, "unit": "state_units"}, "id": "euler_decay_003609_8.5_0.04_1.75_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.04 y with y(0)=8.5, 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) = -0.04 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 8.5, "rate": 0.04, "step": 1.75, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -25.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "53e6e0e35058d42f91ae6312739e41c984123551482787edced5eb70ae8597d7", "difficulty": "medium", "final_answer": {"answer": [2.3, -25.75], "unit": "dimensionless"}, "id": "line_two_point_003632_7.75_22_2.3_-25.75", "license": "Apache-2.0", "prompt": "A line passes through points (7.75, -7.925) and (22, 24.85). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 7.75, "x2": 22.0, "y1": -7.925000000000001, "y2": 24.849999999999994}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.045, 1.68, 2.226], \"unit\": \"temperature_units\"}", "dedupe_signature": "46f68b9c9395c28a4affd94715a8b4e3051478c62540ab1097bde1aacb44c87c", "difficulty": "hard", "final_answer": {"answer": [1.045, 1.68, 2.226], "unit": "temperature_units"}, "id": "heat_step_003647_0.26_1.45_0.2_2.2_2.2_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=1.45, right=2.3; current interior values are [0.2, 2.2, 2.2]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.2, 2.2, 2.2], "left": 1.45, "r": 0.26, "right": 2.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2780 mL to 2.78 L.\n3. Compute M = 4.99 / 2.78.\nFinal: {\"answer\": 1.795, \"unit\": \"mol/L\"}", "dedupe_signature": "3dd9bcb136ab64f622e0c018e7bc0b50c3599a86ffb1ba66c57d79b77fba3336", "difficulty": "medium", "final_answer": {"answer": 1.795, "unit": "mol/L"}, "id": "molarity_003662_4.99_2780", "license": "Apache-2.0", "prompt": "A solution contains 4.99 mol of solute in 2780 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2780 mL to 2.78 L.\nCompute M = 4.99 / 2.78.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.99, "volume_ml": 2780}, "verifier": {"formula": "moles / (volume_ml / 1000)", "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_003670(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_003670\"}", "dedupe_signature": "d1b423035daa67944d6d916b9f06d43be95cec99ab1ef15f25e775ea91042ed2", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_003670"}, "id": "code_003670_normalize_003670", "license": "Apache-2.0", "prompt": "Write a Python function normalize_003670(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": "validation", "task_family": "python_code_generation", "variables": {"function": "normalize_003670"}, "verifier": {"function": "normalize_003670", "tests": ["out = normalize_003670([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_003670([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_003670([1, 1]) == [0.5, 0.5]", "try:\n    normalize_003670([1, -1])\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=69 degrees through the sine of 2 theta.\n3. Substitute v=57.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 223.169, \"unit\": \"m\"}", "dedupe_signature": "99f13c6230b8bbaffd6134fd935616e331653c8dc7a2ceb19ea49c68cbb22ce2", "difficulty": "medium", "final_answer": {"answer": 223.169, "unit": "m"}, "id": "projectile_range_003710_57.2_69", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 57.2 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=57.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 69, "gravity": 9.81, "speed": 57.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.39 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1331.3528, \"unit\": \"g\"}", "dedupe_signature": "01ed5dd71f84fb8a6d7b16992acdc30332342c9af4408383b54e4fd7e50ebaf1", "difficulty": "medium", "final_answer": {"answer": 1331.3528, "unit": "g"}, "id": "stoich_mass_003715_glucose_7.39", "license": "Apache-2.0", "prompt": "A sample contains 7.39 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 = 7.39 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.39}, "verifier": {"formula": "moles * molar_mass", "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 * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 43.83, \"unit\": \"g\"}", "dedupe_signature": "cfab5068eb212d3afd89d5de1c7f86f2969a127bad151f56a9a273df20562c8d", "difficulty": "medium", "final_answer": {"answer": 43.83, "unit": "g"}, "id": "stoich_mass_003769_sodium_chloride_0.75", "license": "Apache-2.0", "prompt": "A sample contains 0.75 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 = 0.75 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.75}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -24.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "066758f94ef0a2706c3ffd302f00fe619b04f68494df520e1abc772179f46e9e", "difficulty": "medium", "final_answer": {"answer": [5.0, -24.75], "unit": "dimensionless"}, "id": "line_two_point_003776_-11.25_-2.5_5_-24.75", "license": "Apache-2.0", "prompt": "A line passes through points (-11.25, -81) and (-2.5, -37.25). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -11.25, "x2": -2.5, "y1": -81.0, "y2": -37.25}, "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_003778(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_003778\"}", "dedupe_signature": "387a80670e375b4de3f1644124863c0d0a8ed0eb6ea6506430333105d3e0d2da", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_003778"}, "id": "code_003778_finite_differences_003778", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_003778(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_003778"}, "verifier": {"function": "finite_differences_003778", "tests": ["assert finite_differences_003778([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_003778([5]) == []", "assert finite_differences_003778([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=321.5 mg, t=236 h, and T_half=56.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 17.7738, \"unit\": \"mg\"}", "dedupe_signature": "df3dfcbb8ca9c42d45f8ac819516c4314deadf1f7adb6834f6b785cb050b853a", "difficulty": "medium", "final_answer": {"answer": 17.7738, "unit": "mg"}, "id": "half_life_003786_321.5_56.5_236", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 321.5 mg. Its half-life is 56.5 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=321.5 mg, t=236 h, and T_half=56.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 236.0, "half_life": 56.5, "initial_amount": 321.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=185.5 V and R=46.1 ohm.\nFinal: {\"answer\": 746.4262, \"unit\": \"W\"}", "dedupe_signature": "489205efffb0431c76d2b409b42800edfdbfcc73c8680a9b0fc35497f7a5d223", "difficulty": "easy", "final_answer": {"answer": 746.4262, "unit": "W"}, "id": "ohm_power_003803_185.5_46.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 46.1 ohm and voltage 185.5 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=185.5 V and R=46.1 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 46.1, "voltage": 185.5}, "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=519 mg, t=123.5 h, and T_half=20 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 7.183, \"unit\": \"mg\"}", "dedupe_signature": "3c06547467f86a7b6213afc39f0c000bca969d6f245009ae5c5fbdb6ff470fd5", "difficulty": "medium", "final_answer": {"answer": 7.183, "unit": "mg"}, "id": "half_life_003804_519_20_123.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 519 mg. Its half-life is 20 hours. How many mg remain after 123.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=519 mg, t=123.5 h, and T_half=20 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 123.5, "half_life": 20.0, "initial_amount": 519.0}, "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(3.8)=-39.28 and f(7.4)=-61.24.\n3. The interval width is 3.6.\nFinal: {\"answer\": -180.936, \"unit\": \"area_units\"}", "dedupe_signature": "99151064139596016b33d4e90c35173a22ce8b331a87ad0a1664b5afd1810a98", "difficulty": "medium", "final_answer": {"answer": -180.936, "unit": "area_units"}, "id": "trapz_linear_003808_-6.1_-16.1_3.8_7.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.1x+-16.1 from x=3.8 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(3.8)=-39.28 and f(7.4)=-61.24.\nThe interval width is 3.6.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -16.1, "slope": -6.1, "x0": 3.8, "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3685 mL to 3.685 L.\n3. Compute M = 4.52 / 3.685.\nFinal: {\"answer\": 1.2266, \"unit\": \"mol/L\"}", "dedupe_signature": "99d557ed298fa543b463a05a46bc1bee78cc9dd32ae448e6a0c6829270b434e6", "difficulty": "medium", "final_answer": {"answer": 1.2266, "unit": "mol/L"}, "id": "molarity_003824_4.52_3685", "license": "Apache-2.0", "prompt": "A solution contains 4.52 mol of solute in 3685 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3685 mL to 3.685 L.\nCompute M = 4.52 / 3.685.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.52, "volume_ml": 3685}, "verifier": {"formula": "moles / (volume_ml / 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": "7d53132299616d6c0fbe519ef9249b42fffc2428d040c4c5f0647cfe4e6853df", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003849_inconsistent_56040f5d_328760", "license": "Apache-2.0", "prompt": "In model card equation case 328760, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"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": "bdfb76826b5b1e5e1c6c4afd0489e6c2f48c1d2af51d4e31a9c645649c652b82", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003867_inconsistent_7481c798_698046", "license": "Apache-2.0", "prompt": "In sensor calibration case 698046, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"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 * 10.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 320.437, \"unit\": \"J\"}", "dedupe_signature": "cefe8beeedd9d2023f1605073d14781e3935f6acccae4be4b0d11ad518366ed1", "difficulty": "easy", "final_answer": {"answer": 320.437, "unit": "J"}, "id": "ke_003871_10.4_7.85", "license": "Apache-2.0", "prompt": "A body of mass 10.4 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 * 10.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.4, "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 = 1425 * 4.45 * 27.\nFinal: {\"answer\": 171213.75, \"unit\": \"J\"}", "dedupe_signature": "aac965165cf1a27cfe6a27c3ae628869b190c9638a38e3c9d8b50ba4f644af30", "difficulty": "easy", "final_answer": {"answer": 171213.75, "unit": "J"}, "id": "heat_q_003874_1425_4.45_27", "license": "Apache-2.0", "prompt": "A 1425 g sample has specific heat 4.45 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 = 1425 * 4.45 * 27.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 27, "heat_capacity": 4.45, "mass_g": 1425}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.3 kg and a = 5.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 81.51, \"unit\": \"N\"}", "dedupe_signature": "1192c374d2e52a12258e5b2625fd6fdec53539f5de71140227a8e01ec7e0f8c4", "difficulty": "easy", "final_answer": {"answer": 81.51, "unit": "N"}, "id": "force_003888_14.3_5.7", "license": "Apache-2.0", "prompt": "A cart has mass 14.3 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 = 14.3 kg and a = 5.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.7, "mass": 14.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.65 kg and a = 7.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 90.2875, \"unit\": \"N\"}", "dedupe_signature": "a40ce1b930504ab2e9127642d9cf36ce453e138b46d80b06292789f3230b3970", "difficulty": "easy", "final_answer": {"answer": 90.2875, "unit": "N"}, "id": "force_003906_11.65_7.75", "license": "Apache-2.0", "prompt": "A cart has mass 11.65 kg and measured acceleration 7.75 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 = 11.65 kg and a = 7.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.75, "mass": 11.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"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 4 steps and round the final state.\nFinal: {\"answer\": 19.0804, \"unit\": \"state_units\"}", "dedupe_signature": "ddc285660cea93cb7e369ffb44060ae03a10fdf4f94d282276fcfb5be77bfec4", "difficulty": "medium", "final_answer": {"answer": 19.0804, "unit": "state_units"}, "id": "euler_decay_003915_71_0.56_0.5_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.56 y with y(0)=71, 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) = -0.56 y, so each step multiplies y by 1 - h*0.56.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 71.0, "rate": 0.56, "step": 0.5, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 19.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "3b50c0d8f5af4d32c03ce7dda91b0220235e3ec3b16503dca15dc24fe2d945bb", "difficulty": "medium", "final_answer": {"answer": [-4.7, 19.25], "unit": "dimensionless"}, "id": "line_two_point_003920_-10_2.25_-4.7_19.25", "license": "Apache-2.0", "prompt": "A line passes through points (-10, 66.25) and (2.25, 8.675). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -10.0, "x2": 2.25, "y1": 66.25, "y2": 8.674999999999999}, "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 slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.75, -5.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "305fbeba225b9b2370d73febcd29eb9df8d36da575b31dfefaaa5dfee78b3efa", "difficulty": "medium", "final_answer": {"answer": [-2.75, -5.0], "unit": "dimensionless"}, "id": "line_two_point_003956_15.5_23_-2.75_-5", "license": "Apache-2.0", "prompt": "A line passes through points (15.5, -47.625) and (23, -68.25). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 15.5, "x2": 23.0, "y1": -47.625, "y2": -68.25}, "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": "87da0f9738d0b97bb19e4f31afc4a6c3bc581594911ea927abd78dec67aff84f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003957_consistent_4153435f_253066", "license": "Apache-2.0", "prompt": "In sensor calibration case 253066, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_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\": [-328.4609, 238.6408], \"unit\": \"N\"}", "dedupe_signature": "64bfdf47e98d87b454446b95ff1c633e9a3825652325a0996b184cb083083320", "difficulty": "medium", "final_answer": {"answer": [-328.4609, 238.6408], "unit": "N"}, "id": "vector_components_003973_406_144", "license": "Apache-2.0", "prompt": "A vector has magnitude 406 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 144, "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. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.62 * 8.314 * 299 / 1.9.\nFinal: {\"answer\": 4736.267, \"unit\": \"kPa\"}", "dedupe_signature": "7c99ed0fbca81050c230845a50cbab2e4768f10b350831253abf115db369cf90", "difficulty": "medium", "final_answer": {"answer": 4736.267, "unit": "kPa"}, "id": "ideal_gas_003999_3.62_299_1.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.62 mol, T=299 K, and V=1.9 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 = 3.62 * 8.314 * 299 / 1.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 3.62, "temp_k": 299, "volume_l": 1.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.685, 1.36, 1.11], \"unit\": \"temperature_units\"}", "dedupe_signature": "6a487570da44fe7440527bfc860461314b306d4e1016ca3602e4592dcf161081", "difficulty": "hard", "final_answer": {"answer": [1.685, 1.36, 1.11], "unit": "temperature_units"}, "id": "heat_step_004007_0.3_1.15_2.6_1.0_0.6_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=1.15, right=1.9; current interior values are [2.6, 1.0, 0.6]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 1.0, 0.6], "left": 1.15, "r": 0.3, "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 165.5 + 273.15.\nFinal: {\"answer\": 438.65, \"unit\": \"K\"}", "dedupe_signature": "db72900096226d586e05cd2414bedd5de5b419aa275cdf6106161b1a72b5f663", "difficulty": "easy", "final_answer": {"answer": 438.65, "unit": "K"}, "id": "unit_convert_004008_c_to_k_165.5", "license": "Apache-2.0", "prompt": "Convert 165.5 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 165.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 165.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.55 * 8.314 * 392 / 44.1.\nFinal: {\"answer\": 410.1573, \"unit\": \"kPa\"}", "dedupe_signature": "a4a6bbe7276fb641e11cd0cf04aca660010ee7793a248c2bd831d9116abb057c", "difficulty": "medium", "final_answer": {"answer": 410.1573, "unit": "kPa"}, "id": "ideal_gas_004017_5.55_392_44.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.55 mol, T=392 K, and V=44.1 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 = 5.55 * 8.314 * 392 / 44.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 5.55, "temp_k": 392, "volume_l": 44.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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)=-25.27 and f(18.4)=-59.68.\n3. The interval width is 9.3.\nFinal: {\"answer\": -395.0175, \"unit\": \"area_units\"}", "dedupe_signature": "3cafe336f3ec18871789718612c285e92b02990083bcc13d8c721664293ce81a", "difficulty": "medium", "final_answer": {"answer": -395.0175, "unit": "area_units"}, "id": "trapz_linear_004024_-3.7_8.4_9.1_18.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.7x+8.4 from x=9.1 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(9.1)=-25.27 and f(18.4)=-59.68.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 8.4, "slope": -3.7, "x0": 9.1, "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. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.71 * 8.314 * 488 / 67.7.\nFinal: {\"answer\": 282.2683, \"unit\": \"kPa\"}", "dedupe_signature": "8cacf551b0d41964e8088c867d20b04f08ecae09aa6d8078ba1ce1ff74eadc1a", "difficulty": "medium", "final_answer": {"answer": 282.2683, "unit": "kPa"}, "id": "ideal_gas_004035_4.71_488_67.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.71 mol, T=488 K, and V=67.7 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 = 4.71 * 8.314 * 488 / 67.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.71, "temp_k": 488, "volume_l": 67.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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(-5.6)=42.3 and f(-1.7)=24.75.\n3. The interval width is 3.9.\nFinal: {\"answer\": 130.7475, \"unit\": \"area_units\"}", "dedupe_signature": "b74e6f4768ef6eff8ef2602c207608def34ffd57e5f6249281f4f38c2cfeccd7", "difficulty": "medium", "final_answer": {"answer": 130.7475, "unit": "area_units"}, "id": "trapz_linear_004042_-4.5_17.1_-5.6_-1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.5x+17.1 from x=-5.6 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(-5.6)=42.3 and f(-1.7)=24.75.\nThe interval width is 3.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 17.1, "slope": -4.5, "x0": -5.6, "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. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1900 * 3.44 * 82.\nFinal: {\"answer\": 535952.0, \"unit\": \"J\"}", "dedupe_signature": "6109134cfb8d86365ac601d045230df12297a8527fde1cbe76287d0cd62e476b", "difficulty": "easy", "final_answer": {"answer": 535952.0, "unit": "J"}, "id": "heat_q_004054_1900_3.44_82", "license": "Apache-2.0", "prompt": "A 1900 g sample has specific heat 3.44 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 = 1900 * 3.44 * 82.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 82, "heat_capacity": 3.44, "mass_g": 1900}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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_004066(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_004066\"}", "dedupe_signature": "065c83aa34e542d34c09cfae1a9009e23fdab51a4e248f100744da1a4a682b5c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_004066"}, "id": "code_004066_normalize_004066", "license": "Apache-2.0", "prompt": "Write a Python function normalize_004066(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": "validation", "task_family": "python_code_generation", "variables": {"function": "normalize_004066"}, "verifier": {"function": "normalize_004066", "tests": ["out = normalize_004066([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_004066([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_004066([1, 1]) == [0.5, 0.5]", "try:\n    normalize_004066([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": "35c02700e1d8befe8481ba264b896523fdcee9ac25a80430cee3478e228caf5c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004067_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 3968 items and budget 79375, 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": "validation", "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. Mass equals amount in moles times molar mass.\n2. Use m = 1.03 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 45.3303, \"unit\": \"g\"}", "dedupe_signature": "412cdb5efe6ef1312f5ee3d66d677e6c4ade6e638c0e5627fa1f52a094b7bb22", "difficulty": "medium", "final_answer": {"answer": 45.3303, "unit": "g"}, "id": "stoich_mass_004075_carbon_dioxide_1.03", "license": "Apache-2.0", "prompt": "A sample contains 1.03 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 = 1.03 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.03}, "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=0.38 and add it to the current value.\nFinal: {\"answer\": [1.263, 0.961, 1.837], \"unit\": \"temperature_units\"}", "dedupe_signature": "0b9104ae88cc086d9281febe8afa1470faa4f559fb9fb4e1cb066cf9c74cca8f", "difficulty": "hard", "final_answer": {"answer": [1.263, 0.961, 1.837], "unit": "temperature_units"}, "id": "heat_step_004079_0.38_2.85_-0.2_0.6_2.35_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=2.85, right=2.75; current interior values are [-0.2, 0.6, 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, 0.6, 2.35], "left": 2.85, "r": 0.38, "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=358 degrees and keep the unit as newtons.\nFinal: {\"answer\": [418.7448, -14.6229], \"unit\": \"N\"}", "dedupe_signature": "ecd80f737f5e0904d111eb57c1bdcd1cbda4b57cb3ccc4eef3d3ac826307bb6d", "difficulty": "medium", "final_answer": {"answer": [418.7448, -14.6229], "unit": "N"}, "id": "vector_components_004081_419_358", "license": "Apache-2.0", "prompt": "A vector has magnitude 419 N at 358 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=358 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 358, "magnitude": 419.0}, "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: 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": "2174635ebd201cc91eff85303ef347282fc3f3ab37dac454916fa95940bf09e7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_004085_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 [1.15, -1.85, 1.5], 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": "validation", "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 = 23^2 and multiply by 0.5 * 1.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 330.625, \"unit\": \"J\"}", "dedupe_signature": "9bc0d2f74a30c72e63dbf37147c1caa4eae787d862bfee070006905b1ea5a974", "difficulty": "easy", "final_answer": {"answer": 330.625, "unit": "J"}, "id": "ke_004087_1.25_23", "license": "Apache-2.0", "prompt": "A body of mass 1.25 kg moves at 23 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23^2 and multiply by 0.5 * 1.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.25, "velocity": 23.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 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 = 4.235 / 2.06.\nFinal: {\"answer\": 2.0558, \"unit\": \"mol/L\"}", "dedupe_signature": "87c954a2ab18cb6d5b980c76f5237e6443ac3c514034efae364be496a2ca0aaf", "difficulty": "medium", "final_answer": {"answer": 2.0558, "unit": "mol/L"}, "id": "molarity_004094_4.235_2060", "license": "Apache-2.0", "prompt": "A solution contains 4.235 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 = 4.235 / 2.06.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.235, "volume_ml": 2060}, "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=0.14 and add it to the current value.\nFinal: {\"answer\": [1.089, -0.657, 1.47], \"unit\": \"temperature_units\"}", "dedupe_signature": "4eb7684ede5155dca1a9e0fcc6af7fa38d9a9a8892f63248f8a48a049961a7ce", "difficulty": "hard", "final_answer": {"answer": [1.089, -0.657, 1.47], "unit": "temperature_units"}, "id": "heat_step_004097_0.14_-0.55_1.95_-1.7_2.1_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=-0.55, right=1.4; current interior values are [1.95, -1.7, 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.95, -1.7, 2.1], "left": -0.55, "r": 0.14, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.7^2 and multiply by 0.5 * 10.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5480.1113, \"unit\": \"J\"}", "dedupe_signature": "c0bc2c99e6ed012c78663fb001da59190527146a2b423c36122e9bc2de7992f0", "difficulty": "easy", "final_answer": {"answer": 5480.1113, "unit": "J"}, "id": "ke_004105_10.25_32.7", "license": "Apache-2.0", "prompt": "A body of mass 10.25 kg moves at 32.7 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 = 32.7^2 and multiply by 0.5 * 10.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.25, "velocity": 32.7}, "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=33 degrees through the sine of 2 theta.\n3. Substitute v=13.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 17.4784, \"unit\": \"m\"}", "dedupe_signature": "9fcbd2c57d147bc551da7c8a1a882a25387d8b8c15280169c0b01a11b89dd396", "difficulty": "medium", "final_answer": {"answer": 17.4784, "unit": "m"}, "id": "projectile_range_004106_13.7_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 13.7 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=13.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "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. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1211.0 / 100.\nFinal: {\"answer\": 12.11, \"unit\": \"m\"}", "dedupe_signature": "471da4d20cc0ae24d5d82fd27d065ab0aad91ad7c3650b3b23fe976350db36e7", "difficulty": "easy", "final_answer": {"answer": 12.11, "unit": "m"}, "id": "unit_convert_004134_cm_to_m_1211", "license": "Apache-2.0", "prompt": "Convert 1211 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 1211.0 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 1211.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=460.5 mg, t=312 h, and T_half=44 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.378, \"unit\": \"mg\"}", "dedupe_signature": "ec3502dd831e92a986ba5c8d3e944b970c9cd1180da52bff4fafb1b30110b13b", "difficulty": "medium", "final_answer": {"answer": 3.378, "unit": "mg"}, "id": "half_life_004146_460.5_44_312", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 460.5 mg. Its half-life is 44 hours. How many mg remain after 312 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=460.5 mg, t=312 h, and T_half=44 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 312.0, "half_life": 44.0, "initial_amount": 460.5}, "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 = 7.02 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 308.9502, \"unit\": \"g\"}", "dedupe_signature": "85d86adde1bc91ea29f1a0beb1857be35c85ba75b6b912442d8747016f07f744", "difficulty": "medium", "final_answer": {"answer": 308.9502, "unit": "g"}, "id": "stoich_mass_004147_carbon_dioxide_7.02", "license": "Apache-2.0", "prompt": "A sample contains 7.02 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 = 7.02 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.02}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=118.1 V and R=42.2 ohm.\nFinal: {\"answer\": 330.5121, \"unit\": \"W\"}", "dedupe_signature": "7069b851b84155e781bb94a61e677a4c2f3258cb6ae02505e28be3c8f22198b0", "difficulty": "easy", "final_answer": {"answer": 330.5121, "unit": "W"}, "id": "ohm_power_004163_118.1_42.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 42.2 ohm and voltage 118.1 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=118.1 V and R=42.2 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 42.2, "voltage": 118.1}, "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) = -0.98 y, so each step multiplies y by 1 - h*0.98.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "bd1658263feb5bd6a92a64f1410cfa7b8f1105b10434791dfc234632c57fae7d", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004167_33.5_0.98_0.9_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.98 y with y(0)=33.5, step size h=0.9, 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) = -0.98 y, so each step multiplies y by 1 - h*0.98.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 33.5, "rate": 0.98, "step": 0.9, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_004174(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_004174\"}", "dedupe_signature": "cd43e285bb21408f8d5ed644ebdc156e3e18843df18795e84cf7cf7b5b0315d3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_004174"}, "id": "code_004174_running_total_004174", "license": "Apache-2.0", "prompt": "Write a Python function running_total_004174(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_004174"}, "verifier": {"function": "running_total_004174", "tests": ["assert running_total_004174([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_004174(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_004174([]) == []"], "type": "python_tests"}}
{"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 11 steps and round the final state.\nFinal: {\"answer\": 2.9247, \"unit\": \"state_units\"}", "dedupe_signature": "f1a5499baa2966625c6abf8da88ad7f118b54c01e8b1b08b5490951403f521e4", "difficulty": "medium", "final_answer": {"answer": 2.9247, "unit": "state_units"}, "id": "euler_decay_004185_56.5_0.59_0.4_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.59 y with y(0)=56.5, 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) = -0.59 y, so each step multiplies y by 1 - h*0.59.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 56.5, "rate": 0.59, "step": 0.4, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=937 mg, t=147 h, and T_half=87.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 292.4214, \"unit\": \"mg\"}", "dedupe_signature": "153711efebc62307a3f8232a596fc902d959f37c265fdbe8c0776b841e796a6c", "difficulty": "medium", "final_answer": {"answer": 292.4214, "unit": "mg"}, "id": "half_life_004200_937_87.5_147", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 937 mg. Its half-life is 87.5 hours. How many mg remain after 147 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=937 mg, t=147 h, and T_half=87.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 147.0, "half_life": 87.5, "initial_amount": 937.0}, "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(9.3)=-17.27 and f(18.4)=-52.76.\n3. The interval width is 9.1.\nFinal: {\"answer\": -318.6365, \"unit\": \"area_units\"}", "dedupe_signature": "65191bc35d0145fd8a524d3bc59448f9ab339fed74574560586ef13ad5c6c317", "difficulty": "medium", "final_answer": {"answer": -318.6365, "unit": "area_units"}, "id": "trapz_linear_004204_-3.9_19_9.3_18.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.9x+19 from x=9.3 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(9.3)=-17.27 and f(18.4)=-52.76.\nThe interval width is 9.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 19.0, "slope": -3.9, "x0": 9.3, "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. 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": "ec00a921dba83b8a305acc9e1a2e9753667b05ae4b084bbb215aad19023bd2f9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004209_inconsistent_74ac0b02_251768", "license": "Apache-2.0", "prompt": "In instrument manual case 251768, 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": "validation", "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 = 7.25 kg and a = 1.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 7.975, \"unit\": \"N\"}", "dedupe_signature": "dc6349c8daa1b265c9ea8533cc83ed8cd9206a02c0164294dc249e72ff5c3e63", "difficulty": "easy", "final_answer": {"answer": 7.975, "unit": "N"}, "id": "force_004212_7.25_1.1", "license": "Apache-2.0", "prompt": "A cart has mass 7.25 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 = 7.25 kg and a = 1.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.1, "mass": 7.25}, "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 = 2.99 * 8.314 * 618 / 11.8.\nFinal: {\"answer\": 1301.9301, \"unit\": \"kPa\"}", "dedupe_signature": "bfbd46f36625c07494bb2ca54dab68c2f462e34520f363f626f2c03106b33bb4", "difficulty": "medium", "final_answer": {"answer": 1301.9301, "unit": "kPa"}, "id": "ideal_gas_004215_2.99_618_11.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.99 mol, T=618 K, and V=11.8 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 = 2.99 * 8.314 * 618 / 11.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.99, "temp_k": 618, "volume_l": 11.8}, "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 = 95 * 3.995 * 24.\nFinal: {\"answer\": 9108.6, \"unit\": \"J\"}", "dedupe_signature": "e8d0a98b59d903cfe1ba8d0e284ff69c7bb4266cd1b21db688946f82cad5726d", "difficulty": "easy", "final_answer": {"answer": 9108.6, "unit": "J"}, "id": "heat_q_004234_95_3.995_24", "license": "Apache-2.0", "prompt": "A 95 g sample has specific heat 3.995 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 = 95 * 3.995 * 24.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 24, "heat_capacity": 3.995, "mass_g": 95}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"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\": 0.1308, \"unit\": \"state_units\"}", "dedupe_signature": "cb874c4adf0158bc5d74428c0b3f5ef9d83b20d43f78593b4aebfa170b243ff8", "difficulty": "medium", "final_answer": {"answer": 0.1308, "unit": "state_units"}, "id": "euler_decay_004239_75.5_0.86_1.4_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.86 y with y(0)=75.5, step size h=1.4, 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 75.5, "rate": 0.86, "step": 1.4, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.1^2 and multiply by 0.5 * 19.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7160.4975, \"unit\": \"J\"}", "dedupe_signature": "a3e07092d037fd69254051ecdc94ce60c3a4400c206c7e882c1e0f4c4bf05955", "difficulty": "easy", "final_answer": {"answer": 7160.4975, "unit": "J"}, "id": "ke_004249_19.5_27.1", "license": "Apache-2.0", "prompt": "A body of mass 19.5 kg moves at 27.1 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 = 27.1^2 and multiply by 0.5 * 19.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.5, "velocity": 27.1}, "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=7.4 V and R=115.2 ohm.\nFinal: {\"answer\": 0.4753, \"unit\": \"W\"}", "dedupe_signature": "5b0966a5bdf409976a733f6df4143866f3fa83c78785289f9ed5ba72cfb380cc", "difficulty": "easy", "final_answer": {"answer": 0.4753, "unit": "W"}, "id": "ohm_power_004253_7.4_115.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 115.2 ohm and voltage 7.4 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=7.4 V and R=115.2 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 115.2, "voltage": 7.4}, "verifier": {"formula": "voltage ** 2 / resistance", "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 4881.0 / 100.\nFinal: {\"answer\": 48.81, \"unit\": \"m\"}", "dedupe_signature": "298123df670d2c3dc43fb507c0e9c788a12bc92ab86f2ec6323a5e63c41ddadb", "difficulty": "easy", "final_answer": {"answer": 48.81, "unit": "m"}, "id": "unit_convert_004260_cm_to_m_4881", "license": "Apache-2.0", "prompt": "Convert 4881 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 4881.0 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 4881.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.838, 1.315, -0.276], \"unit\": \"temperature_units\"}", "dedupe_signature": "c5b184c3d1a693579b4c1b2b6dc962ade489a389b790c5114d5fb20edd4f050d", "difficulty": "hard", "final_answer": {"answer": [1.838, 1.315, -0.276], "unit": "temperature_units"}, "id": "heat_step_004295_0.22_0.8_2.3_1.7_-0.65_-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=0.8, right=-1.3; current interior values are [2.3, 1.7, -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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.3, 1.7, -0.65], "left": 0.8, "r": 0.22, "right": -1.3}, "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\": [4.55, 14.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "d8c54068cb64b5bbe41113950b6a882ffad84c1c87c5a6626555fe515218624f", "difficulty": "medium", "final_answer": {"answer": [4.55, 14.5], "unit": "dimensionless"}, "id": "line_two_point_004316_-14.5_-0.25_4.55_14.5", "license": "Apache-2.0", "prompt": "A line passes through points (-14.5, -51.475) and (-0.25, 13.3625). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -14.5, "x2": -0.25, "y1": -51.474999999999994, "y2": 13.3625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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=75.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 557.8469, \"unit\": \"m\"}", "dedupe_signature": "eb5714c1e8b262e55d8e378ff9852347f6522c45f0d11d4b1f5be9a9ded69668", "difficulty": "medium", "final_answer": {"answer": 557.8469, "unit": "m"}, "id": "projectile_range_004322_75.1_52", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 75.1 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=75.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 52, "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. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 230.0 + 273.15.\nFinal: {\"answer\": 503.15, \"unit\": \"K\"}", "dedupe_signature": "cf7440c5826a87e4109480f174f80f25770852f30a373ebd5066a3adf314047b", "difficulty": "easy", "final_answer": {"answer": 503.15, "unit": "K"}, "id": "unit_convert_004332_c_to_k_230", "license": "Apache-2.0", "prompt": "Convert 230 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 230.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 230.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"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\": 24.1039, \"unit\": \"state_units\"}", "dedupe_signature": "1d68ee8cb2b8a28ac65cde46dadcba68f0c5630856cec4e39cc5ba89e2b4211c", "difficulty": "medium", "final_answer": {"answer": 24.1039, "unit": "state_units"}, "id": "euler_decay_004365_37_0.93_0.05_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.93 y with y(0)=37, step size h=0.05, 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) = -0.93 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 37.0, "rate": 0.93, "step": 0.05, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.9 kg and a = 0.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 0.95, \"unit\": \"N\"}", "dedupe_signature": "ebc4fb3957ecd1714fbe96bdd390bb2e03e32b219cfbe3c03cca96ef03508e90", "difficulty": "easy", "final_answer": {"answer": 0.95, "unit": "N"}, "id": "force_004374_1.9_0.5", "license": "Apache-2.0", "prompt": "A cart has mass 1.9 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 = 1.9 kg and a = 0.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.5, "mass": 1.9}, "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 = 1690 * 3.33 * 52.\nFinal: {\"answer\": 292640.4, \"unit\": \"J\"}", "dedupe_signature": "6bd166d10a4a5adc969be848c0aa3c1969a314617ac110d60b48f69d2ac73318", "difficulty": "easy", "final_answer": {"answer": 292640.4, "unit": "J"}, "id": "heat_q_004396_1690_3.33_52", "license": "Apache-2.0", "prompt": "A 1690 g sample has specific heat 3.33 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 = 1690 * 3.33 * 52.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 52, "heat_capacity": 3.33, "mass_g": 1690}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"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 11 steps and round the final state.\nFinal: {\"answer\": 0.0003, \"unit\": \"state_units\"}", "dedupe_signature": "3a3808d1764605c8bff6c2be2ebcd2a8651cfe9bc65ba6c754e4ca66237cbc26", "difficulty": "medium", "final_answer": {"answer": 0.0003, "unit": "state_units"}, "id": "euler_decay_004401_71.5_0.56_1.2_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.56 y with y(0)=71.5, 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) = -0.56 y, so each step multiplies y by 1 - h*0.56.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 71.5, "rate": 0.56, "step": 1.2, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_004408(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_004408\"}", "dedupe_signature": "8123b643177a55c7aec36f4bcd11c74aecdaa946a01216b9fff328f5966dc557", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_004408"}, "id": "code_004408_pairwise_ratios_004408", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_004408(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": "validation", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_004408"}, "verifier": {"function": "pairwise_ratios_004408", "tests": ["assert pairwise_ratios_004408([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_004408([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_004408([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=99 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-2.1901, 13.8276], \"unit\": \"N\"}", "dedupe_signature": "151b7e0572a39576f14455732c459f5d3586819ee2fc02484b2de567ca25ad52", "difficulty": "medium", "final_answer": {"answer": [-2.1901, 13.8276], "unit": "N"}, "id": "vector_components_004423_14_99", "license": "Apache-2.0", "prompt": "A vector has magnitude 14 N at 99 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=99 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 99, "magnitude": 14.0}, "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. Use Newton's second law F = m a.\n2. Substitute m = 2.1 kg and a = 0.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 1.26, \"unit\": \"N\"}", "dedupe_signature": "bf05b887db008d55ba89bce23d0533d89235c2d92df9f41fdae296b598dec289", "difficulty": "easy", "final_answer": {"answer": 1.26, "unit": "N"}, "id": "force_004446_2.1_0.6", "license": "Apache-2.0", "prompt": "A cart has mass 2.1 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 = 2.1 kg and a = 0.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.6, "mass": 2.1}, "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 = 5.39 * 8.314 * 280 / 104.9.\nFinal: {\"answer\": 119.6138, \"unit\": \"kPa\"}", "dedupe_signature": "78d626ebf5002fa42bc31daf4082e39d6a3d0dfcf0a2791346a5e44c2acfd4fe", "difficulty": "medium", "final_answer": {"answer": 119.6138, "unit": "kPa"}, "id": "ideal_gas_004449_5.39_280_104.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.39 mol, T=280 K, and V=104.9 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 = 5.39 * 8.314 * 280 / 104.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 5.39, "temp_k": 280, "volume_l": 104.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.95^2 and multiply by 0.5 * 7.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1151.8739, \"unit\": \"J\"}", "dedupe_signature": "ca3c456ebacb33f9dc446fd12acaae589acab79067f0f21eb1a44cf67645751d", "difficulty": "easy", "final_answer": {"answer": 1151.8739, "unit": "J"}, "id": "ke_004465_7.15_17.95", "license": "Apache-2.0", "prompt": "A body of mass 7.15 kg moves at 17.95 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 = 17.95^2 and multiply by 0.5 * 7.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.15, "velocity": 17.95}, "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=66.3 V and R=124.5 ohm.\nFinal: {\"answer\": 35.3067, \"unit\": \"W\"}", "dedupe_signature": "4a4bc3ab938e494c1e65fa2734def467b2173dce9e47210daf257e79d42332ca", "difficulty": "easy", "final_answer": {"answer": 35.3067, "unit": "W"}, "id": "ohm_power_004487_66.3_124.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 124.5 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=124.5 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 124.5, "voltage": 66.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [-252.7947, 212.1199], \"unit\": \"N\"}", "dedupe_signature": "a0cf027155794b61470b294f6688df7d5f4b898e905789e3a435bf66c4d21094", "difficulty": "medium", "final_answer": {"answer": [-252.7947, 212.1199], "unit": "N"}, "id": "vector_components_004495_330_140", "license": "Apache-2.0", "prompt": "A vector has magnitude 330 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 140, "magnitude": 330.0}, "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. 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=78.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 596.3082, \"unit\": \"m\"}", "dedupe_signature": "7e227cd5ae58bf65b4855b771e7c3711ca78f11a410fb872d03fa29f2442bcaa", "difficulty": "medium", "final_answer": {"answer": 596.3082, "unit": "m"}, "id": "projectile_range_004502_78.9_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 78.9 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=78.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "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. 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\": [-143.8749, -79.7512], \"unit\": \"N\"}", "dedupe_signature": "0ae14048fd00da31ea05a4864942fb44de7037f1d6862f16eb6d8d600e9714aa", "difficulty": "medium", "final_answer": {"answer": [-143.8749, -79.7512], "unit": "N"}, "id": "vector_components_004513_164.5_209", "license": "Apache-2.0", "prompt": "A vector has magnitude 164.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 209, "magnitude": 164.5}, "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 = 17.3^2 and multiply by 0.5 * 18.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2768.4325, \"unit\": \"J\"}", "dedupe_signature": "03ada929c2ade54d1f8b76c2460bbec0b8e16f9d4cf1a876965b37cc2db1a681", "difficulty": "easy", "final_answer": {"answer": 2768.4325, "unit": "J"}, "id": "ke_004519_18.5_17.3", "license": "Apache-2.0", "prompt": "A body of mass 18.5 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 * 18.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.5, "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=58 degrees through the sine of 2 theta.\n3. Substitute v=76.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 536.1842, \"unit\": \"m\"}", "dedupe_signature": "d883104af7ee04cfb30e62f4c6c0205f89d9b5ee85ee30f0bda29deccd894d6d", "difficulty": "medium", "final_answer": {"answer": 536.1842, "unit": "m"}, "id": "projectile_range_004520_76.5_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 76.5 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=76.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 76.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 26.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "c112c8384da09e6a4c617a6dd44cbd4db24f470f3e07a1f025a3ec143c07a47f", "difficulty": "medium", "final_answer": {"answer": [-5.65, 26.0], "unit": "dimensionless"}, "id": "line_two_point_004532_10.25_17.25_-5.65_26", "license": "Apache-2.0", "prompt": "A line passes through points (10.25, -31.9125) and (17.25, -71.4625). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 10.25, "x2": 17.25, "y1": -31.9125, "y2": -71.4625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - 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": "2e18d0fb855e118e379ccaf13bd2b6e2e2f7f0f3df97344a85aa7ae9674ec068", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004533_inconsistent_1e14b074_918100", "license": "Apache-2.0", "prompt": "In sensor calibration case 918100, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 895 * 2.605 * 81.\nFinal: {\"answer\": 188849.475, \"unit\": \"J\"}", "dedupe_signature": "ddb9a9b01da70427a4de50f9e43fe8ed9335b0be7a0dc4082c3ef51e36ab381d", "difficulty": "easy", "final_answer": {"answer": 188849.475, "unit": "J"}, "id": "heat_q_004540_895_2.605_81", "license": "Apache-2.0", "prompt": "A 895 g sample has specific heat 2.605 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 = 895 * 2.605 * 81.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 81, "heat_capacity": 2.605, "mass_g": 895}, "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 1190 mL to 1.19 L.\n3. Compute M = 0.585 / 1.19.\nFinal: {\"answer\": 0.4916, \"unit\": \"mol/L\"}", "dedupe_signature": "298dcbdfad554621544277d97c6b35d30c7f221fb07c57b52fb622b74ce6a682", "difficulty": "medium", "final_answer": {"answer": 0.4916, "unit": "mol/L"}, "id": "molarity_004544_0.585_1190", "license": "Apache-2.0", "prompt": "A solution contains 0.585 mol of solute in 1190 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1190 mL to 1.19 L.\nCompute M = 0.585 / 1.19.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 0.585, "volume_ml": 1190}, "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)=-28.33 and f(-3.2)=-12.52.\n3. The interval width is 3.1.\nFinal: {\"answer\": -63.3175, \"unit\": \"area_units\"}", "dedupe_signature": "acd07a8bf5f215e71b52ea08a6511dbbb2cd972ce9e44f73646ffcbeee12124e", "difficulty": "medium", "final_answer": {"answer": -63.3175, "unit": "area_units"}, "id": "trapz_linear_004546_5.1_3.8_-6.3_-3.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.1x+3.8 from x=-6.3 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(-6.3)=-28.33 and f(-3.2)=-12.52.\nThe interval width is 3.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 3.8, "slope": 5.1, "x0": -6.3, "x1": -3.1999999999999997}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "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": "ac5bc816c506ef04c2a6ef19d4ee5f78dfe973f14f26f784e4846492a61dadd0", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004587_inconsistent_c1271127_83029", "license": "Apache-2.0", "prompt": "In quality-control check case 83029, 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": "validation", "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_004588(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_004588\"}", "dedupe_signature": "7de6ddd0efc8f12b036043c8d83e13d767b763b2e4745b90b4632569e6bf58f0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_004588"}, "id": "code_004588_unit_vector_004588", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_004588(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": "validation", "task_family": "python_code_generation", "variables": {"function": "unit_vector_004588"}, "verifier": {"function": "unit_vector_004588", "tests": ["ux, uy = unit_vector_004588(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_004588(0, 5) == (0, 1)", "try:\n    unit_vector_004588(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "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 V and R=98.6 ohm.\nFinal: {\"answer\": 225.1623, \"unit\": \"W\"}", "dedupe_signature": "5f3cfc661e9edebd2dfe5700570a5d47eb0ca3f4775c5355cafbb7e851497e51", "difficulty": "easy", "final_answer": {"answer": 225.1623, "unit": "W"}, "id": "ohm_power_004595_149_98.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 98.6 ohm and voltage 149 V across it. Compute the dissipated power 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 V and R=98.6 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 98.6, "voltage": 149.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.25 kg and a = 4.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 74.175, \"unit\": \"N\"}", "dedupe_signature": "fbd0836955da7f80f38dc5ebfcb27936b4806cc1aa1dad858fef92da061304be", "difficulty": "easy", "final_answer": {"answer": 74.175, "unit": "N"}, "id": "force_004608_17.25_4.3", "license": "Apache-2.0", "prompt": "A cart has mass 17.25 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 = 17.25 kg and a = 4.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.3, "mass": 17.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [2.04, 1.23, 1.14], \"unit\": \"temperature_units\"}", "dedupe_signature": "e899a3f0f415abaca89abbdb9a3fc96abc5b7aa7fb9b5c4a6bfdf6bd44e8b035", "difficulty": "hard", "final_answer": {"answer": [2.04, 1.23, 1.14], "unit": "temperature_units"}, "id": "heat_step_004637_0.4_1.25_2.6_2.55_-0.8_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=1.25, right=0.7; current interior values are [2.6, 2.55, -0.8]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 2.55, -0.8], "left": 1.25, "r": 0.4, "right": 0.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.45 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 19.8045, \"unit\": \"g\"}", "dedupe_signature": "dee8d6f7b0b557b1dd6ed2af327c955fd40c56140f2e10d2792f028d729d5db6", "difficulty": "medium", "final_answer": {"answer": 19.8045, "unit": "g"}, "id": "stoich_mass_004651_carbon_dioxide_0.45", "license": "Apache-2.0", "prompt": "A sample contains 0.45 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 = 0.45 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.45}, "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(-0.4)=12.86 and f(6.6)=-14.44.\n3. The interval width is 7.\nFinal: {\"answer\": -5.53, \"unit\": \"area_units\"}", "dedupe_signature": "24bfede4bc4d744d2b9efb5f3d6d4c9370923ab26eb90353e0e5f925fbe963b7", "difficulty": "medium", "final_answer": {"answer": -5.53, "unit": "area_units"}, "id": "trapz_linear_004690_-3.9_11.3_-0.4_6.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.9x+11.3 from x=-0.4 to x=6.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.4)=12.86 and f(6.6)=-14.44.\nThe interval width is 7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 11.3, "slope": -3.9, "x0": -0.4, "x1": 6.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The 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, -3.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "ef33fe45bed912e95788d605ba85c3312cd02f5c353832a86cc858850c03a493", "difficulty": "medium", "final_answer": {"answer": [-8.35, -3.0], "unit": "dimensionless"}, "id": "line_two_point_004694_-10_-7.5_-8.35_-3", "license": "Apache-2.0", "prompt": "A line passes through points (-10, 80.5) and (-7.5, 59.625). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -10.0, "x2": -7.5, "y1": 80.5, "y2": 59.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 40 mL to 0.04 L.\n3. Compute M = 0.115 / 0.04.\nFinal: {\"answer\": 2.875, \"unit\": \"mol/L\"}", "dedupe_signature": "239a9bc3a46361ac977cb9562ba6ab6a4846fb616c457a961cf86f2df8ad2ee2", "difficulty": "medium", "final_answer": {"answer": 2.875, "unit": "mol/L"}, "id": "molarity_004706_0.115_40", "license": "Apache-2.0", "prompt": "A solution contains 0.115 mol of solute in 40 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 40 mL to 0.04 L.\nCompute M = 0.115 / 0.04.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 0.115, "volume_ml": 40}, "verifier": {"formula": "moles / (volume_ml / 1000)", "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": "5bcc0ba7403a809aaf57a467166b503e9bd109686f7700f53f7a33826b1a11bb", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004715_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 19.4 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": "validation", "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 = 4.45^2 and multiply by 0.5 * 29.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 295.5523, \"unit\": \"J\"}", "dedupe_signature": "412de52cbb4f1ed32ec27125a015e9782616ba4d53b9235a4695744225fb7872", "difficulty": "easy", "final_answer": {"answer": 295.5523, "unit": "J"}, "id": "ke_004717_29.85_4.45", "license": "Apache-2.0", "prompt": "A body of mass 29.85 kg moves at 4.45 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 = 4.45^2 and multiply by 0.5 * 29.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.85, "velocity": 4.45}, "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 = 475 * 3.295 * 80.\nFinal: {\"answer\": 125210.0, \"unit\": \"J\"}", "dedupe_signature": "33033504feb56e78c1dc275c5cd2753f4727e413ea94c03850f6c3439ddf958b", "difficulty": "easy", "final_answer": {"answer": 125210.0, "unit": "J"}, "id": "heat_q_004720_475_3.295_80", "license": "Apache-2.0", "prompt": "A 475 g sample has specific heat 3.295 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 = 475 * 3.295 * 80.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 80, "heat_capacity": 3.295, "mass_g": 475}, "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 275 mL to 0.275 L.\n3. Compute M = 2.97 / 0.275.\nFinal: {\"answer\": 10.8, \"unit\": \"mol/L\"}", "dedupe_signature": "0fd15e554827bbf9fa2e7ad4a6615aded6165514d4203e849198242f0d540906", "difficulty": "medium", "final_answer": {"answer": 10.8, "unit": "mol/L"}, "id": "molarity_004724_2.97_275", "license": "Apache-2.0", "prompt": "A solution contains 2.97 mol of solute in 275 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 275 mL to 0.275 L.\nCompute M = 2.97 / 0.275.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.97, "volume_ml": 275}, "verifier": {"formula": "moles / (volume_ml / 1000)", "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 2420.0 / 100.\nFinal: {\"answer\": 24.2, \"unit\": \"m\"}", "dedupe_signature": "acb4e1e4fc117f7c49fc4c79765cca1601859e7a4391955ca7eba8f027d39e21", "difficulty": "easy", "final_answer": {"answer": 24.2, "unit": "m"}, "id": "unit_convert_004728_cm_to_m_2420", "license": "Apache-2.0", "prompt": "Convert 2420 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 2420.0 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 2420.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "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=68.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 383.5813, \"unit\": \"m\"}", "dedupe_signature": "286d38fef78579f4a8fce79a74116fec433cec336f536a52b0b2f72408b0ca6a", "difficulty": "medium", "final_answer": {"answer": 383.5813, "unit": "m"}, "id": "projectile_range_004754_68.2_63", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 68.2 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=68.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 63, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=414.5 mg, t=214.5 h, and T_half=39.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.6121, \"unit\": \"mg\"}", "dedupe_signature": "86ca9ae38cd66c149341bc0d2d16c3577ab889a18515d715aa83f173f529f53f", "difficulty": "medium", "final_answer": {"answer": 9.6121, "unit": "mg"}, "id": "half_life_004758_414.5_39.5_214.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 414.5 mg. Its half-life is 39.5 hours. How many mg remain after 214.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=414.5 mg, t=214.5 h, and T_half=39.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 214.5, "half_life": 39.5, "initial_amount": 414.5}, "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 1935 mL to 1.935 L.\n3. Compute M = 2.455 / 1.935.\nFinal: {\"answer\": 1.2687, \"unit\": \"mol/L\"}", "dedupe_signature": "d59bf49310c713394105a3a17e82cfbd3613442d4d380dbadefe4ad4a4526912", "difficulty": "medium", "final_answer": {"answer": 1.2687, "unit": "mol/L"}, "id": "molarity_004760_2.455_1935", "license": "Apache-2.0", "prompt": "A solution contains 2.455 mol of solute in 1935 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1935 mL to 1.935 L.\nCompute M = 2.455 / 1.935.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.455, "volume_ml": 1935}, "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=0.1 and add it to the current value.\nFinal: {\"answer\": [-1.405, -1.73, -1.355], \"unit\": \"temperature_units\"}", "dedupe_signature": "2f85a72270f6a6dab469af0376b2957348d2922b28903a5ffcd633885e870bff", "difficulty": "hard", "final_answer": {"answer": [-1.405, -1.73, -1.355], "unit": "temperature_units"}, "id": "heat_step_004763_0.1_0.9_-1.65_-1.75_-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=0.9, right=1.4; current interior values are [-1.65, -1.75, -1.65]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-1.65, -1.75, -1.65], "left": 0.9, "r": 0.1, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [2.072, -0.486, 0.478], \"unit\": \"temperature_units\"}", "dedupe_signature": "3b074284e706966ae49af491d2ffaff3843cab5b61041a8fa42c6f99aefd41c0", "difficulty": "hard", "final_answer": {"answer": [2.072, -0.486, 0.478], "unit": "temperature_units"}, "id": "heat_step_004781_0.08_2.6_2.3_-0.85_0.55_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=2.6, right=1.05; current interior values are [2.3, -0.85, 0.55]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.3, -0.85, 0.55], "left": 2.6, "r": 0.08, "right": 1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.89 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1061.1188, \"unit\": \"g\"}", "dedupe_signature": "acfaa0eff427ff3cabbe6edda89c84bdfc17fc765afa6c7bb4ec8e6f8f4e1393", "difficulty": "medium", "final_answer": {"answer": 1061.1188, "unit": "g"}, "id": "stoich_mass_004795_glucose_5.89", "license": "Apache-2.0", "prompt": "A sample contains 5.89 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 = 5.89 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.89}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [393.46, -20.6204], \"unit\": \"N\"}", "dedupe_signature": "8c93359f412f930e698212c10cef9caf6698f294219485d3660c4b1ae9f2db00", "difficulty": "medium", "final_answer": {"answer": [393.46, -20.6204], "unit": "N"}, "id": "vector_components_004801_394_357", "license": "Apache-2.0", "prompt": "A vector has magnitude 394 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 357, "magnitude": 394.0}, "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": "cf6770d2e424521361dc6c446562d4e3f32a088b038d624a40b3d5cb006e1c7c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004803_consistent_03f5e041_802997", "license": "Apache-2.0", "prompt": "In quality-control check case 802997, 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": "validation", "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_004804(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_004804\"}", "dedupe_signature": "65f840ab9a29f6e28f7690376f1cfad90a716be48fe36de615232cf73d274c23", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_004804"}, "id": "code_004804_finite_differences_004804", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_004804(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_004804"}, "verifier": {"function": "finite_differences_004804", "tests": ["assert finite_differences_004804([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_004804([5]) == []", "assert finite_differences_004804([]) == []"], "type": "python_tests"}}
{"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)=-25.68 and f(-0.4)=-15.24.\n3. The interval width is 2.9.\nFinal: {\"answer\": -59.334, \"unit\": \"area_units\"}", "dedupe_signature": "ba944270279c814a0fd181cad37c26ac60badd6a56316a2bfa0ab17357541a17", "difficulty": "medium", "final_answer": {"answer": -59.334, "unit": "area_units"}, "id": "trapz_linear_004816_3.6_-13.8_-3.3_-0.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.6x+-13.8 from x=-3.3 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(-3.3)=-25.68 and f(-0.4)=-15.24.\nThe interval width is 2.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -13.8, "slope": 3.6, "x0": -3.3, "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. The function contract has a 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_004822(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_004822\"}", "dedupe_signature": "b436aba74d1932a1629b1764ed41a5331f249d6e17128be809b6035777a32435", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004822"}, "id": "code_004822_safe_mean_004822", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004822(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": "validation", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004822"}, "verifier": {"function": "safe_mean_004822", "tests": ["assert safe_mean_004822([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004822(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004822([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R 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 * 594 / 30.2.\nFinal: {\"answer\": 883.0459, \"unit\": \"kPa\"}", "dedupe_signature": "19a6599576eb2942c1d4a11598899b6ab40a8741cbf06b03a807cf47ccc329c2", "difficulty": "medium", "final_answer": {"answer": 883.0459, "unit": "kPa"}, "id": "ideal_gas_004827_5.4_594_30.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.4 mol, T=594 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 = 5.4 * 8.314 * 594 / 30.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 5.4, "temp_k": 594, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=83 mg, t=191 h, and T_half=98 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 21.4969, \"unit\": \"mg\"}", "dedupe_signature": "3d0c936bc27d0596c33d38d0752f9e24273aa2545cf644811f787d0f93ee4d4f", "difficulty": "medium", "final_answer": {"answer": 21.4969, "unit": "mg"}, "id": "half_life_004848_83_98_191", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 83 mg. Its half-life is 98 hours. How many mg remain after 191 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=83 mg, t=191 h, and T_half=98 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 191.0, "half_life": 98.0, "initial_amount": 83.0}, "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(8.5)=51.3 and f(16.1)=86.26.\n3. The interval width is 7.6.\nFinal: {\"answer\": 522.728, \"unit\": \"area_units\"}", "dedupe_signature": "ebcdd0074993ac631de04401e39c2f4f763e2dd17d9bcef5a2d86e000d631129", "difficulty": "medium", "final_answer": {"answer": 522.728, "unit": "area_units"}, "id": "trapz_linear_004852_4.6_12.2_8.5_16.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.6x+12.2 from x=8.5 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(8.5)=51.3 and f(16.1)=86.26.\nThe interval width is 7.6.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 12.2, "slope": 4.6, "x0": 8.5, "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. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.3^2 and multiply by 0.5 * 8.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1188.9627, \"unit\": \"J\"}", "dedupe_signature": "2fe6adfc0f4725d767b60f825b5ca43aba17b7c7ad6c1f470e547a45503d3157", "difficulty": "easy", "final_answer": {"answer": 1188.9627, "unit": "J"}, "id": "ke_004861_8.95_16.3", "license": "Apache-2.0", "prompt": "A body of mass 8.95 kg moves at 16.3 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 = 16.3^2 and multiply by 0.5 * 8.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.95, "velocity": 16.3}, "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 = 0.8 * 8.314 * 296 / 94.2.\nFinal: {\"answer\": 20.8997, \"unit\": \"kPa\"}", "dedupe_signature": "7e5cc1b5fd6b3d6b98ca81d780fba3555e004a65c658e97158934e0caefbe00f", "difficulty": "medium", "final_answer": {"answer": 20.8997, "unit": "kPa"}, "id": "ideal_gas_004863_0.8_296_94.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.8 mol, T=296 K, and V=94.2 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 = 0.8 * 8.314 * 296 / 94.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.8, "temp_k": 296, "volume_l": 94.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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_004894(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_004894\"}", "dedupe_signature": "cb0e091b2e11722d814c8f00eda7ef958fd884cbcbb73c2799587e05ecae530a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_004894"}, "id": "code_004894_finite_differences_004894", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_004894(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_004894"}, "verifier": {"function": "finite_differences_004894", "tests": ["assert finite_differences_004894([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_004894([5]) == []", "assert finite_differences_004894([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4120 mL to 4.12 L.\n3. Compute M = 4.02 / 4.12.\nFinal: {\"answer\": 0.9757, \"unit\": \"mol/L\"}", "dedupe_signature": "b1ae8223ef48cc36bbb6563ca314b71b14c32c2cffae5ac67db852498b18b67b", "difficulty": "medium", "final_answer": {"answer": 0.9757, "unit": "mol/L"}, "id": "molarity_004904_4.02_4120", "license": "Apache-2.0", "prompt": "A solution contains 4.02 mol of solute in 4120 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4120 mL to 4.12 L.\nCompute M = 4.02 / 4.12.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.02, "volume_ml": 4120}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "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=84.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 569.4916, \"unit\": \"m\"}", "dedupe_signature": "75aa98c1e08081e97b7ddb1d40c7222509db5d344836834bfc1b2f628f15b8a6", "difficulty": "medium", "final_answer": {"answer": 569.4916, "unit": "m"}, "id": "projectile_range_004916_84.2_64", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 84.2 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=84.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 64, "gravity": 9.81, "speed": 84.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "0ba8df2e2a4280ede22a6f863aba869015f67b7ff3276b14dde5bf6cfb930502", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004923_15.5_0.64_1.75_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.64 y with y(0)=15.5, 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) = -0.64 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 15.5, "rate": 0.64, "step": 1.75, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_004930(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_004930\"}", "dedupe_signature": "22c74ae03615cf89b37bf780980c0b4af5e0d5ffd875fb7bf572e79863c4da78", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_004930"}, "id": "code_004930_finite_differences_004930", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_004930(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_004930"}, "verifier": {"function": "finite_differences_004930", "tests": ["assert finite_differences_004930([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_004930([5]) == []", "assert finite_differences_004930([]) == []"], "type": "python_tests"}}
{"category": "science_math_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 * 1.39 * 79.\nFinal: {\"answer\": 127379.6, \"unit\": \"J\"}", "dedupe_signature": "cbfe26517e6e430ac1df15bdeadf03a189bb175dfed277650ee618c6d39c8245", "difficulty": "easy", "final_answer": {"answer": 127379.6, "unit": "J"}, "id": "heat_q_004936_1160_1.39_79", "license": "Apache-2.0", "prompt": "A 1160 g sample has specific heat 1.39 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 = 1160 * 1.39 * 79.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 1.39, "mass_g": 1160}, "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=733.5 mg, t=68 h, and T_half=5.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1392, \"unit\": \"mg\"}", "dedupe_signature": "ba85e03e1f842eccf036d0d5d25db016fb3eaab186d76945ebde3dd9266825ae", "difficulty": "medium", "final_answer": {"answer": 0.1392, "unit": "mg"}, "id": "half_life_004938_733.5_5.5_68", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 733.5 mg. Its half-life is 5.5 hours. How many mg remain after 68 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=733.5 mg, t=68 h, and T_half=5.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 68.0, "half_life": 5.5, "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 4165 mL to 4.165 L.\n3. Compute M = 1.07 / 4.165.\nFinal: {\"answer\": 0.2569, \"unit\": \"mol/L\"}", "dedupe_signature": "738e4378fbbad7e86711523299cc7aa8ef6715594d7a1eb85133e104555fbdd1", "difficulty": "medium", "final_answer": {"answer": 0.2569, "unit": "mol/L"}, "id": "molarity_004940_1.07_4165", "license": "Apache-2.0", "prompt": "A solution contains 1.07 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 = 1.07 / 4.165.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 1.07, "volume_ml": 4165}, "verifier": {"formula": "moles / (volume_ml / 1000)", "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": "85f42c2fb28b9bffb1edc90d9640b8af3c20dfc40b3256cc36c90b2888ccfebd", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004967_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory experiment record from batch 38771 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": "validation", "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. 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\": 5.3435, \"unit\": \"state_units\"}", "dedupe_signature": "675dab6ed0ae81eb25a4b1ac0c7ef2b7bd3f6b490eb80cdbb5cddfe88c51ec89", "difficulty": "medium", "final_answer": {"answer": 5.3435, "unit": "state_units"}, "id": "euler_decay_004977_47_0.89_0.3_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.89 y with y(0)=47, 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) = -0.89 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 47.0, "rate": 0.89, "step": 0.3, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_004984(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_004984\"}", "dedupe_signature": "db5d7cbce9787cf637871b1534dbb101f4143054690a697b2b466bde40ccefc4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_004984"}, "id": "code_004984_center_values_004984", "license": "Apache-2.0", "prompt": "Write a Python function center_values_004984(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": "validation", "task_family": "python_code_generation", "variables": {"function": "center_values_004984"}, "verifier": {"function": "center_values_004984", "tests": ["out = center_values_004984([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_004984([5]) == [0]", "try:\n    center_values_004984([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [2.261, 0.698, -0.017], \"unit\": \"temperature_units\"}", "dedupe_signature": "7ad0d55cf3d14527433156f2460375ea1ca1c87808b6681472777ee79e7ca37d", "difficulty": "hard", "final_answer": {"answer": [2.261, 0.698, -0.017], "unit": "temperature_units"}, "id": "heat_step_005015_0.42_2.85_1.4_2.0_-0.5_-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 [1.4, 2.0, -0.5]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, 2.0, -0.5], "left": 2.85, "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=10 degrees and keep the unit as newtons.\nFinal: {\"answer\": [278.2082, 49.0556], \"unit\": \"N\"}", "dedupe_signature": "0b9c25418a1cb3bdcd65078568af963f58634256f16ca369b4d57d1f4f447bcd", "difficulty": "medium", "final_answer": {"answer": [278.2082, 49.0556], "unit": "N"}, "id": "vector_components_005017_282.5_10", "license": "Apache-2.0", "prompt": "A vector has magnitude 282.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 10, "magnitude": 282.5}, "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, 16.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "31092718c17b35a1ad8fae0394bfba0044b6abff833181b7cc487a6871693f68", "difficulty": "medium", "final_answer": {"answer": [8.8, 16.5], "unit": "dimensionless"}, "id": "line_two_point_005018_-3_0.5_8.8_16.5", "license": "Apache-2.0", "prompt": "A line passes through points (-3, -9.9) and (0.5, 20.9). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -3.0, "x2": 0.5, "y1": -9.900000000000002, "y2": 20.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=180 mg, t=159.5 h, and T_half=16 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1796, \"unit\": \"mg\"}", "dedupe_signature": "68bfb39e56f6098c076d099a6a482b8522e09a56760577659029a778e9f6ab14", "difficulty": "medium", "final_answer": {"answer": 0.1796, "unit": "mg"}, "id": "half_life_005028_180_16_159.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 180 mg. Its half-life is 16 hours. How many mg remain after 159.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=180 mg, t=159.5 h, and T_half=16 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 159.5, "half_life": 16.0, "initial_amount": 180.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [9.5459, -9.5459], \"unit\": \"N\"}", "dedupe_signature": "d31de9675732fb7ae62812e92f5947f17c7e1d46898be8041aaa8cb22d4b2116", "difficulty": "medium", "final_answer": {"answer": [9.5459, -9.5459], "unit": "N"}, "id": "vector_components_005035_13.5_315", "license": "Apache-2.0", "prompt": "A vector has magnitude 13.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 315, "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 function contract has a 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_005074(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_005074\"}", "dedupe_signature": "394ff7efccd6f45a380db3e31dac42b17d18405e3c99ed0a7529ff9bde6522a5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_005074"}, "id": "code_005074_safe_mean_005074", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_005074(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": "validation", "task_family": "python_code_generation", "variables": {"function": "safe_mean_005074"}, "verifier": {"function": "safe_mean_005074", "tests": ["assert safe_mean_005074([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_005074(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_005074([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [2.08, -0.165, -0.793], \"unit\": \"temperature_units\"}", "dedupe_signature": "9496c21c792636b25b182609b0f6a342d13d4b2385f5487f1480815f89e578b0", "difficulty": "hard", "final_answer": {"answer": [2.08, -0.165, -0.793], "unit": "temperature_units"}, "id": "heat_step_005087_0.02_-1.4_2.2_-0.2_-0.85_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=-1.4, right=1.35; current interior values are [2.2, -0.2, -0.85]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.2, -0.2, -0.85], "left": -1.4, "r": 0.02, "right": 1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=14 degrees through the sine of 2 theta.\n3. Substitute v=29.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 41.9299, \"unit\": \"m\"}", "dedupe_signature": "face505be8e3b7482d22531ec09c1efcb90464d3a4af8d446ce71ccf641e4931", "difficulty": "medium", "final_answer": {"answer": 41.9299, "unit": "m"}, "id": "projectile_range_005114_29.6_14", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 29.6 m/s and angle 14 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=14 degrees through the sine of 2 theta.\nSubstitute v=29.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 14, "gravity": 9.81, "speed": 29.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.16 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 126.2304, \"unit\": \"g\"}", "dedupe_signature": "4ab4246489a92084f320cfa6277a0e26790f60555a40e139cbaad69ed09bf4c6", "difficulty": "medium", "final_answer": {"answer": 126.2304, "unit": "g"}, "id": "stoich_mass_005119_sodium_chloride_2.16", "license": "Apache-2.0", "prompt": "A sample contains 2.16 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 = 2.16 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.16}, "verifier": {"formula": "moles * molar_mass", "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 3504.5 / 100.\nFinal: {\"answer\": 35.045, \"unit\": \"m\"}", "dedupe_signature": "3a668c106ad9dff12e1f3b6bc92d502fb23c79328b55c8b3e9cf7107f10453df", "difficulty": "easy", "final_answer": {"answer": 35.045, "unit": "m"}, "id": "unit_convert_005124_cm_to_m_3504.5", "license": "Apache-2.0", "prompt": "Convert 3504.5 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 3504.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 3504.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "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=81.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 469.1925, \"unit\": \"m\"}", "dedupe_signature": "131dd219d1bed792d9322d6c09a19128ffdfb4a1278f1e3eac9a622237ecd69c", "difficulty": "medium", "final_answer": {"answer": 469.1925, "unit": "m"}, "id": "projectile_range_005150_81.4_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.4 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=81.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "gravity": 9.81, "speed": 81.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.6)=18.06 and f(-3.2)=14.22.\n3. The interval width is 6.4.\nFinal: {\"answer\": 103.296, \"unit\": \"area_units\"}", "dedupe_signature": "1120e423cac52a46264c50f3dee86f61a3a6fc1eaa74ea363e8d428b98e40ab4", "difficulty": "medium", "final_answer": {"answer": 103.296, "unit": "area_units"}, "id": "trapz_linear_005158_-0.6_12.3_-9.6_-3.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+12.3 from x=-9.6 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(-9.6)=18.06 and f(-3.2)=14.22.\nThe interval width is 6.4.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 12.3, "slope": -0.6, "x0": -9.6, "x1": -3.1999999999999993}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8.2^2 and multiply by 0.5 * 18.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 606.841, \"unit\": \"J\"}", "dedupe_signature": "84e2a4420d47f666724b6133fa144537f978550d245c85ba0a69ad7c1e2aecf5", "difficulty": "easy", "final_answer": {"answer": 606.841, "unit": "J"}, "id": "ke_005167_18.05_8.2", "license": "Apache-2.0", "prompt": "A body of mass 18.05 kg moves at 8.2 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 = 8.2^2 and multiply by 0.5 * 18.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.05, "velocity": 8.2}, "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 = 4.06 * 8.314 * 394 / 42.3.\nFinal: {\"answer\": 314.4068, \"unit\": \"kPa\"}", "dedupe_signature": "f350063bf347c4b57644bcb1d9002c743b94a53c9b9a0f2851c39aa97bc3f783", "difficulty": "medium", "final_answer": {"answer": 314.4068, "unit": "kPa"}, "id": "ideal_gas_005169_4.06_394_42.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.06 mol, T=394 K, and V=42.3 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 = 4.06 * 8.314 * 394 / 42.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.06, "temp_k": 394, "volume_l": 42.3}, "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 = 955 * 4.8 * 42.\nFinal: {\"answer\": 192528.0, \"unit\": \"J\"}", "dedupe_signature": "6ccf94d2256d94d74287ce99db03464e69cc9f5dfb700bbd4184a8415179487e", "difficulty": "easy", "final_answer": {"answer": 192528.0, "unit": "J"}, "id": "heat_q_005170_955_4.8_42", "license": "Apache-2.0", "prompt": "A 955 g sample has specific heat 4.8 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 = 955 * 4.8 * 42.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 42, "heat_capacity": 4.8, "mass_g": 955}, "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 = 7.35 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1324.1466, \"unit\": \"g\"}", "dedupe_signature": "074e40ba4c40ddf7ea8304668cc2a193ee51346f58b7edf79119421c8cc12f0c", "difficulty": "medium", "final_answer": {"answer": 1324.1466, "unit": "g"}, "id": "stoich_mass_005173_glucose_7.35", "license": "Apache-2.0", "prompt": "A sample contains 7.35 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 = 7.35 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.35}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 6.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "783d2a4b8987c05855e2cc6da06120f6a8f21d5e39bdd4e848a26e574e19f941", "difficulty": "medium", "final_answer": {"answer": [-5.8, 6.25], "unit": "dimensionless"}, "id": "line_two_point_005180_2.5_8.5_-5.8_6.25", "license": "Apache-2.0", "prompt": "A line passes through points (2.5, -8.25) and (8.5, -43.05). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 2.5, "x2": 8.5, "y1": -8.25, "y2": -43.05}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "f249756f191b997d537e7efd32ddc5f6280cf6cfd84816ddae72be12f5889836", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005183_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, 2.1, -1.65], 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": "validation", "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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.2)=-3.62 and f(3.7)=22.12.\n3. The interval width is 3.9.\nFinal: {\"answer\": 36.075, \"unit\": \"area_units\"}", "dedupe_signature": "5b43d8bb2517455137fdeaa2b125987f6ac126765d2a72ed1f0aa90d6ce4e590", "difficulty": "medium", "final_answer": {"answer": 36.075, "unit": "area_units"}, "id": "trapz_linear_005194_6.6_-2.3_-0.2_3.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+-2.3 from x=-0.2 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(-0.2)=-3.62 and f(3.7)=22.12.\nThe interval width is 3.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -2.3, "slope": 6.6, "x0": -0.2, "x1": 3.6999999999999997}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "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_005200(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_005200\"}", "dedupe_signature": "ceb226cba0e150814e9557d429a797d22470a7f728eab5b2a63ea1fc2947a867", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_005200"}, "id": "code_005200_pairwise_ratios_005200", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_005200(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": "validation", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_005200"}, "verifier": {"function": "pairwise_ratios_005200", "tests": ["assert pairwise_ratios_005200([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_005200([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_005200([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": "bb2c52e3de08a44cba7a61d203ed01159dcdf228f2cb2edc82c1edb4e5e3a7cb", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_005201_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=34.5 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": "validation", "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 the ideal gas law P V = n R 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 * 598 / 15.5.\nFinal: {\"answer\": 1190.0177, \"unit\": \"kPa\"}", "dedupe_signature": "7608c80ac0d4e11847b7eb0432622ca22398d25ef310d54e92a1376d94835fb6", "difficulty": "medium", "final_answer": {"answer": 1190.0177, "unit": "kPa"}, "id": "ideal_gas_005205_3.71_598_15.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.71 mol, T=598 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 = 3.71 * 8.314 * 598 / 15.5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 3.71, "temp_k": 598, "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 = 1415 * 4.31 * 35.\nFinal: {\"answer\": 213452.75, \"unit\": \"J\"}", "dedupe_signature": "e1cd98c21f0393befa1be4c4001d65ab3623d81b4a98521b864d26e836daf60a", "difficulty": "easy", "final_answer": {"answer": 213452.75, "unit": "J"}, "id": "heat_q_005206_1415_4.31_35", "license": "Apache-2.0", "prompt": "A 1415 g sample has specific heat 4.31 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 = 1415 * 4.31 * 35.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 35, "heat_capacity": 4.31, "mass_g": 1415}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.27 y, so each step multiplies y by 1 - h*0.27.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0714, \"unit\": \"state_units\"}", "dedupe_signature": "d4b515897d36a3ff6abcf94fea1b63ffca08925f86939ab44f0256f8884832cc", "difficulty": "medium", "final_answer": {"answer": 0.0714, "unit": "state_units"}, "id": "euler_decay_005211_0.5_0.27_0.8_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.27 y with y(0)=0.5, step size h=0.8, 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) = -0.27 y, so each step multiplies y by 1 - h*0.27.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 0.5, "rate": 0.27, "step": 0.8, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_005218(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_005218\"}", "dedupe_signature": "ac5168f705adf3a6d77934fba54b9dda21c38e79a2d3aa081a7addc2a8d2bdcf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_005218"}, "id": "code_005218_finite_differences_005218", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_005218(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_005218"}, "verifier": {"function": "finite_differences_005218", "tests": ["assert finite_differences_005218([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_005218([5]) == []", "assert finite_differences_005218([]) == []"], "type": "python_tests"}}
{"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 5 steps and round the final state.\nFinal: {\"answer\": -0.0627, \"unit\": \"state_units\"}", "dedupe_signature": "67c2a2e20571fc2bebaa458e764a3f32e5291d6fd2bdd3bd8a5d2216ba3b312c", "difficulty": "medium", "final_answer": {"answer": -0.0627, "unit": "state_units"}, "id": "euler_decay_005229_75.5_0.69_1.8_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.69 y with y(0)=75.5, step size h=1.8, 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) = -0.69 y, so each step multiplies y by 1 - h*0.69.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 75.5, "rate": 0.69, "step": 1.8, "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\": [1.328, 0.388, 1.19], \"unit\": \"temperature_units\"}", "dedupe_signature": "28400b668ef90751eb598608a454671f851affd1b18727e44bcd30ddf70e69c5", "difficulty": "hard", "final_answer": {"answer": [1.328, 0.388, 1.19], "unit": "temperature_units"}, "id": "heat_step_005249_0.04_-1.6_1.5_0.3_1.3_-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=-1.6, right=-0.45; current interior values are [1.5, 0.3, 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, 0.3, 1.3], "left": -1.6, "r": 0.04, "right": -0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.35 kg and a = 14.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 166.2775, \"unit\": \"N\"}", "dedupe_signature": "c2d6f90ac1602e867da433dc132c65d51e931e74e00fbf2203d238c885581f53", "difficulty": "easy", "final_answer": {"answer": 166.2775, "unit": "N"}, "id": "force_005256_11.35_14.65", "license": "Apache-2.0", "prompt": "A cart has mass 11.35 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 = 11.35 kg and a = 14.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.65, "mass": 11.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-1.454, 1.422, -0.912], \"unit\": \"temperature_units\"}", "dedupe_signature": "836f809e9045c40a41797ca88e68c863559805c68c663d038406f2149da8723d", "difficulty": "hard", "final_answer": {"answer": [-1.454, 1.422, -0.912], "unit": "temperature_units"}, "id": "heat_step_005267_0.44_-1.65_0.9_-1.9_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=-1.65, right=-0.95; current interior values are [0.9, -1.9, 2.85]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.9, -1.9, 2.85], "left": -1.65, "r": 0.44, "right": -0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R 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 * 616 / 17.5.\nFinal: {\"answer\": 1062.3297, \"unit\": \"kPa\"}", "dedupe_signature": "b6bf5a3b4526c0206ddfb83943d34021cddcda73e7e7c4035cfc092d55675a3f", "difficulty": "medium", "final_answer": {"answer": 1062.3297, "unit": "kPa"}, "id": "ideal_gas_005277_3.63_616_17.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.63 mol, T=616 K, and V=17.5 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 * 616 / 17.5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 3.63, "temp_k": 616, "volume_l": 17.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 9.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "e45069540329d5dcf88c9be39958609ea419d3a8ee2399547066ba18d95cb46f", "difficulty": "medium", "final_answer": {"answer": [-0.5, 9.5], "unit": "dimensionless"}, "id": "line_two_point_005288_-14.25_-6.75_-0.5_9.5", "license": "Apache-2.0", "prompt": "A line passes through points (-14.25, 16.625) and (-6.75, 12.875). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -14.25, "x2": -6.75, "y1": 16.625, "y2": 12.875}, "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 pairwise_ratios_005290(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_005290\"}", "dedupe_signature": "8b6fe9d78e8a7e0084e02a0f4a8c0ba0a1848f8dbe99417bfa099208ba1460d7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_005290"}, "id": "code_005290_pairwise_ratios_005290", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_005290(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": "validation", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_005290"}, "verifier": {"function": "pairwise_ratios_005290", "tests": ["assert pairwise_ratios_005290([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_005290([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_005290([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": "3e5fa1c1acb971595de72510dbab4f0d82c0898efca9df8a0705bdcb94dd1de7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005291_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 [-1.55, -0.1, 0.8], 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": "validation", "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. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=227 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-42.2839, -45.3439], \"unit\": \"N\"}", "dedupe_signature": "0dd70c0fdb66ecbcd092a1ac5d06713faf90bc5595576d3aa3f6578b2c5ba8ba", "difficulty": "medium", "final_answer": {"answer": [-42.2839, -45.3439], "unit": "N"}, "id": "vector_components_005305_62_227", "license": "Apache-2.0", "prompt": "A vector has magnitude 62 N at 227 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=227 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 227, "magnitude": 62.0}, "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. Use Newton's second law F = m a.\n2. Substitute m = 4.15 kg and a = 6.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 28.4275, \"unit\": \"N\"}", "dedupe_signature": "02fa8a0df9fb0cde95d88da8a16918222beae073b2c32a1783dd62c2c710b216", "difficulty": "easy", "final_answer": {"answer": 28.4275, "unit": "N"}, "id": "force_005310_4.15_6.85", "license": "Apache-2.0", "prompt": "A cart has mass 4.15 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 = 4.15 kg and a = 6.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.85, "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 = 28.3^2 and multiply by 0.5 * 12.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5025.5847, \"unit\": \"J\"}", "dedupe_signature": "c35d49345c5f3fb8b69337a03d4fa68b72dddd9d7016e2b71296f6195136a633", "difficulty": "easy", "final_answer": {"answer": 5025.5847, "unit": "J"}, "id": "ke_005311_12.55_28.3", "license": "Apache-2.0", "prompt": "A body of mass 12.55 kg moves at 28.3 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 = 28.3^2 and multiply by 0.5 * 12.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.55, "velocity": 28.3}, "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 = 1820 * 1.915 * 42.\nFinal: {\"answer\": 146382.6, \"unit\": \"J\"}", "dedupe_signature": "fe09ce2a4ff1f6015444da013093f141df25e6cabd852eb46e057b018a78fde7", "difficulty": "easy", "final_answer": {"answer": 146382.6, "unit": "J"}, "id": "heat_q_005314_1820_1.915_42", "license": "Apache-2.0", "prompt": "A 1820 g sample has specific heat 1.915 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 = 1820 * 1.915 * 42.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 42, "heat_capacity": 1.915, "mass_g": 1820}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 4.35^2 and multiply by 0.5 * 0.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2.8384, \"unit\": \"J\"}", "dedupe_signature": "37179bef8dfd272fa2485f10b1f54c8434f9c2af11574676b6509b478e8c3c5a", "difficulty": "easy", "final_answer": {"answer": 2.8384, "unit": "J"}, "id": "ke_005329_0.3_4.35", "license": "Apache-2.0", "prompt": "A body of mass 0.3 kg moves at 4.35 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 = 4.35^2 and multiply by 0.5 * 0.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.3, "velocity": 4.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "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": "3ecd46fa6e8816114ea6b73fbb10434bd36dfec3f7256e9936fa063a108e9330", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005343_inconsistent_56040f5d_69115", "license": "Apache-2.0", "prompt": "In student derivation case 69115, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "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 V and R=124.2 ohm.\nFinal: {\"answer\": 260.8696, \"unit\": \"W\"}", "dedupe_signature": "db30d9e0158ac157a00751dc5f70c7d56555602d7a1dea0b905169838a76e17a", "difficulty": "easy", "final_answer": {"answer": 260.8696, "unit": "W"}, "id": "ohm_power_005351_180_124.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 124.2 ohm and voltage 180 V across it. Compute the dissipated power 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 V and R=124.2 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 124.2, "voltage": 180.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=160 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-409.2361, 148.9498], \"unit\": \"N\"}", "dedupe_signature": "161587b3a3ec21c3fb6e1f216782a6d292964e8c1b64e9338d1fec0958bf904b", "difficulty": "medium", "final_answer": {"answer": [-409.2361, 148.9498], "unit": "N"}, "id": "vector_components_005359_435.5_160", "license": "Apache-2.0", "prompt": "A vector has magnitude 435.5 N at 160 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=160 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 160, "magnitude": 435.5}, "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 clamp_005362(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_005362\"}", "dedupe_signature": "9857a93aa7f5eaf50df8148dd72a6ce401d1dcea908cf3a901b47487834db71b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005362"}, "id": "code_005362_clamp_005362", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005362(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": "validation", "task_family": "python_code_generation", "variables": {"function": "clamp_005362"}, "verifier": {"function": "clamp_005362", "tests": ["assert clamp_005362(5, 0, 10) == 5", "assert clamp_005362(-2, 0, 10) == 0", "assert clamp_005362(12, 0, 10) == 10", "try:\n    clamp_005362(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 = 15.5^2 and multiply by 0.5 * 24.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2925.0438, \"unit\": \"J\"}", "dedupe_signature": "4a0997dbf3153ec703f8c28d9bf119a73cb78d7203751f230a25da94ebe95f87", "difficulty": "easy", "final_answer": {"answer": 2925.0438, "unit": "J"}, "id": "ke_005365_24.35_15.5", "license": "Apache-2.0", "prompt": "A body of mass 24.35 kg moves at 15.5 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 = 15.5^2 and multiply by 0.5 * 24.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.35, "velocity": 15.5}, "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 = 1775 * 0.77 * 93.\nFinal: {\"answer\": 127107.75, \"unit\": \"J\"}", "dedupe_signature": "040b10a9353e8b4a946e87e50a2b47a3238c61b9dd2708b6e1319b7b0a08eb52", "difficulty": "easy", "final_answer": {"answer": 127107.75, "unit": "J"}, "id": "heat_q_005368_1775_0.77_93", "license": "Apache-2.0", "prompt": "A 1775 g sample has specific heat 0.77 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 = 1775 * 0.77 * 93.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 93, "heat_capacity": 0.77, "mass_g": 1775}, "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 = 6.32 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1138.5859, \"unit\": \"g\"}", "dedupe_signature": "3b136a67a0b104183ba139496b58f13bfdba1f96d05cb115df8f7017069991fa", "difficulty": "medium", "final_answer": {"answer": 1138.5859, "unit": "g"}, "id": "stoich_mass_005371_glucose_6.32", "license": "Apache-2.0", "prompt": "A sample contains 6.32 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 = 6.32 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.32}, "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=0.08 and add it to the current value.\nFinal: {\"answer\": [0.64, 2.14, 0.256], \"unit\": \"temperature_units\"}", "dedupe_signature": "bb969c068526eff2175efffeaac0b6c95e6d434658e43d8c65796775da502c1c", "difficulty": "hard", "final_answer": {"answer": [0.64, 2.14, 0.256], "unit": "temperature_units"}, "id": "heat_step_005375_0.08_0.25_0.5_2.5_0.0_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=0.25, right=0.7; current interior values are [0.5, 2.5, 0.0]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.5, 2.5, 0.0], "left": 0.25, "r": 0.08, "right": 0.7}, "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\": [-7.1, 19.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "f8c853c484e6bbe6487f342425c06debfc7b31145e4ec721a8981ba132a734b6", "difficulty": "medium", "final_answer": {"answer": [-7.1, 19.75], "unit": "dimensionless"}, "id": "line_two_point_005378_-1.75_-0.75_-7.1_19.75", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, 32.175) and (-0.75, 25.075). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": -0.75, "y1": 32.175, "y2": 25.075}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16^2 and multiply by 0.5 * 22.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2822.4, \"unit\": \"J\"}", "dedupe_signature": "8005e938578d11f9ce9a05f1a60c8c771d4eb783024cd9de4c5d676deaee9b40", "difficulty": "easy", "final_answer": {"answer": 2822.4, "unit": "J"}, "id": "ke_005383_22.05_16", "license": "Apache-2.0", "prompt": "A body of mass 22.05 kg moves at 16 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16^2 and multiply by 0.5 * 22.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.05, "velocity": 16.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"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 6 steps and round the final state.\nFinal: {\"answer\": 6.1953, \"unit\": \"state_units\"}", "dedupe_signature": "b0cd3b2a1cdb18183863ecfb0ad4b8e67ae2b577c02389152842cb8e14e0476d", "difficulty": "medium", "final_answer": {"answer": 6.1953, "unit": "state_units"}, "id": "euler_decay_005391_65.5_0.65_0.5_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.65 y with y(0)=65.5, step size h=0.5, 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) = -0.65 y, so each step multiplies y by 1 - h*0.65.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 65.5, "rate": 0.65, "step": 0.5, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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 mg, t=68.5 h, and T_half=41 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 240.2819, \"unit\": \"mg\"}", "dedupe_signature": "50fd8f29ac2fe3eaa575e4cddb7c403dcf9a66c69f3f09a50849b5f077fc7e6f", "difficulty": "medium", "final_answer": {"answer": 240.2819, "unit": "mg"}, "id": "half_life_005406_765_41_68.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 765 mg. Its half-life is 41 hours. How many mg remain after 68.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=765 mg, t=68.5 h, and T_half=41 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 68.5, "half_life": 41.0, "initial_amount": 765.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "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": "a8d19f55062cc70bc4298b045a90415952c9bfe69dbd0b0716ab1b5140ed12f2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005417_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.23 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": "validation", "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 = 8.75^2 and multiply by 0.5 * 25.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 985.7422, \"unit\": \"J\"}", "dedupe_signature": "57e067dbee582d5a77f21c2925fc6c104ed1e017ca62016db54f5478d19b1dad", "difficulty": "easy", "final_answer": {"answer": 985.7422, "unit": "J"}, "id": "ke_005419_25.75_8.75", "license": "Apache-2.0", "prompt": "A body of mass 25.75 kg moves at 8.75 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 = 8.75^2 and multiply by 0.5 * 25.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.75, "velocity": 8.75}, "verifier": {"formula": "0.5 * mass * velocity ** 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 292.0 / 100.\nFinal: {\"answer\": 2.92, \"unit\": \"m\"}", "dedupe_signature": "48a2c63eba4b42b5206567b42b8047adcc62e65718fe1b0726134668c370db38", "difficulty": "easy", "final_answer": {"answer": 2.92, "unit": "m"}, "id": "unit_convert_005430_cm_to_m_292", "license": "Apache-2.0", "prompt": "Convert 292 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 292.0 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 292.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.3 kg and a = 3.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 46.665, \"unit\": \"N\"}", "dedupe_signature": "3b0d103c5859c2190458ddca0768c60a78fc7b1c620f5ea5f52b52e9a35c30cd", "difficulty": "easy", "final_answer": {"answer": 46.665, "unit": "N"}, "id": "force_005436_15.3_3.05", "license": "Apache-2.0", "prompt": "A cart has mass 15.3 kg and measured acceleration 3.05 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 = 15.3 kg and a = 3.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.05, "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 = 2.8^2 and multiply by 0.5 * 26.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 103.096, \"unit\": \"J\"}", "dedupe_signature": "2963cc234ad87e71aa70c9ca3575e22f87c3f70cd6ac2634c8aded1b9b35e941", "difficulty": "easy", "final_answer": {"answer": 103.096, "unit": "J"}, "id": "ke_005437_26.3_2.8", "license": "Apache-2.0", "prompt": "A body of mass 26.3 kg moves at 2.8 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 = 2.8^2 and multiply by 0.5 * 26.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.3, "velocity": 2.8}, "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 = 1290 * 0.965 * 23.\nFinal: {\"answer\": 28631.55, \"unit\": \"J\"}", "dedupe_signature": "0445084f6891fad1afccf3a2658489c6425b8a1f9aeddc37943a0af4a0a03f03", "difficulty": "easy", "final_answer": {"answer": 28631.55, "unit": "J"}, "id": "heat_q_005458_1290_0.965_23", "license": "Apache-2.0", "prompt": "A 1290 g sample has specific heat 0.965 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 = 1290 * 0.965 * 23.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 23, "heat_capacity": 0.965, "mass_g": 1290}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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)=20.37 and f(8.8)=25.06.\n3. The interval width is 6.7.\nFinal: {\"answer\": 152.1905, \"unit\": \"area_units\"}", "dedupe_signature": "d33923eacab365442b1aae02827b78e3e127f26116fa0ab127f0f4bf734717c7", "difficulty": "medium", "final_answer": {"answer": 152.1905, "unit": "area_units"}, "id": "trapz_linear_005464_0.7_18.9_2.1_8.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+18.9 from x=2.1 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(2.1)=20.37 and f(8.8)=25.06.\nThe interval width is 6.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 18.9, "slope": 0.7, "x0": 2.1, "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=0.32 and add it to the current value.\nFinal: {\"answer\": [0.232, 1.206, 1.762], \"unit\": \"temperature_units\"}", "dedupe_signature": "881c2c303bef18d418359db444cbe8029269aa4647fa613066dd06e75264b900", "difficulty": "hard", "final_answer": {"answer": [0.232, 1.206, 1.762], "unit": "temperature_units"}, "id": "heat_step_005465_0.32_-0.4_-0.2_1.35_2.45_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=-0.4, right=1.4; current interior values are [-0.2, 1.35, 2.45]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, 1.35, 2.45], "left": -0.4, "r": 0.32, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=362.5 mg, t=207.5 h, and T_half=105.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 92.7331, \"unit\": \"mg\"}", "dedupe_signature": "5b2de417fd208010af8cd9afcd1ea31daddc1193f6a2e51c500f9ff87f00f118", "difficulty": "medium", "final_answer": {"answer": 92.7331, "unit": "mg"}, "id": "half_life_005496_362.5_105.5_207.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 362.5 mg. Its half-life is 105.5 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=362.5 mg, t=207.5 h, and T_half=105.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 207.5, "half_life": 105.5, "initial_amount": 362.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.593, 0.26, 0.944], \"unit\": \"temperature_units\"}", "dedupe_signature": "15c021a223d00317d2d05672724f882d7343929699af595722e68c540238b3a1", "difficulty": "hard", "final_answer": {"answer": [0.593, 0.26, 0.944], "unit": "temperature_units"}, "id": "heat_step_005501_0.26_0.9_1.1_-0.65_1.1_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=0.9, right=2.25; current interior values are [1.1, -0.65, 1.1]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.1, -0.65, 1.1], "left": 0.9, "r": 0.26, "right": 2.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 90 * 4.04 * 60.\nFinal: {\"answer\": 21816.0, \"unit\": \"J\"}", "dedupe_signature": "a73defe06524b4c813be6002039a437c1ba1a63569ea4bd132773163583f84c0", "difficulty": "easy", "final_answer": {"answer": 21816.0, "unit": "J"}, "id": "heat_q_005512_90_4.04_60", "license": "Apache-2.0", "prompt": "A 90 g sample has specific heat 4.04 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 = 90 * 4.04 * 60.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 60, "heat_capacity": 4.04, "mass_g": 90}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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": "f6a80fd9ed73ebbc2f2b5bd519fd4fdb8b9bf0b3bbc8433073903851faa04d43", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_005525_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 13.9 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": "validation", "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=72 degrees through the sine of 2 theta.\n3. Substitute v=29.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 53.5663, \"unit\": \"m\"}", "dedupe_signature": "25a036f8b54aae77373adcb521e554de589dcb8c911cad0c558b6fda10aaeeff", "difficulty": "medium", "final_answer": {"answer": 53.5663, "unit": "m"}, "id": "projectile_range_005528_29.9_72", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 29.9 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=29.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 72, "gravity": 9.81, "speed": 29.9}, "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 = 940 * 2.41 * 10.\nFinal: {\"answer\": 22654.0, \"unit\": \"J\"}", "dedupe_signature": "1ae9d50fc0ac01f000fc1111127c7a29f64e26300bf393bff3aa00381c99b5e5", "difficulty": "easy", "final_answer": {"answer": 22654.0, "unit": "J"}, "id": "heat_q_005530_940_2.41_10", "license": "Apache-2.0", "prompt": "A 940 g sample has specific heat 2.41 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 = 940 * 2.41 * 10.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 10, "heat_capacity": 2.41, "mass_g": 940}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.388, 0.066, -1.126], \"unit\": \"temperature_units\"}", "dedupe_signature": "ed2d6f31e3bb7011d55a5e57c042ac13ef17105dbddc3170c7b7ee2ac2777bd7", "difficulty": "hard", "final_answer": {"answer": [0.388, 0.066, -1.126], "unit": "temperature_units"}, "id": "heat_step_005537_0.44_2.2_-0.8_-1.1_1.25_-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=2.2, right=-1.8; current interior values are [-0.8, -1.1, 1.25]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.8, -1.1, 1.25], "left": 2.2, "r": 0.44, "right": -1.8}, "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 running_total_005542(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_005542\"}", "dedupe_signature": "44743a0e350a2facf0cb06914232d2b80d98bf6c02ee911354d611d0d9632ba8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_005542"}, "id": "code_005542_running_total_005542", "license": "Apache-2.0", "prompt": "Write a Python function running_total_005542(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_005542"}, "verifier": {"function": "running_total_005542", "tests": ["assert running_total_005542([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_005542(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_005542([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3050 mL to 3.05 L.\n3. Compute M = 3.035 / 3.05.\nFinal: {\"answer\": 0.9951, \"unit\": \"mol/L\"}", "dedupe_signature": "fcbe5b98f4a2580c7270f5091b5da8112a2840e024f4c301c8dcef55b41dde7d", "difficulty": "medium", "final_answer": {"answer": 0.9951, "unit": "mol/L"}, "id": "molarity_005552_3.035_3050", "license": "Apache-2.0", "prompt": "A solution contains 3.035 mol of solute in 3050 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3050 mL to 3.05 L.\nCompute M = 3.035 / 3.05.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.035, "volume_ml": 3050}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.45 kg and a = 11.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 97.175, \"unit\": \"N\"}", "dedupe_signature": "bc8a14fd3c63fb3cc75a837943e0951447032e424f8a05291a7d0b0aeaa29f16", "difficulty": "easy", "final_answer": {"answer": 97.175, "unit": "N"}, "id": "force_005562_8.45_11.5", "license": "Apache-2.0", "prompt": "A cart has mass 8.45 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 = 8.45 kg and a = 11.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.5, "mass": 8.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1955 mL to 1.955 L.\n3. Compute M = 2.7 / 1.955.\nFinal: {\"answer\": 1.3811, \"unit\": \"mol/L\"}", "dedupe_signature": "2f054bccfd94c623d3705b3e686e9c65fe2c4c2b5d0fade8f7c26a3f86f8e155", "difficulty": "medium", "final_answer": {"answer": 1.3811, "unit": "mol/L"}, "id": "molarity_005570_2.7_1955", "license": "Apache-2.0", "prompt": "A solution contains 2.7 mol of solute in 1955 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1955 mL to 1.955 L.\nCompute M = 2.7 / 1.955.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.7, "volume_ml": 1955}, "verifier": {"formula": "moles / (volume_ml / 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=27 degrees and keep the unit as newtons.\nFinal: {\"answer\": [65.9345, 33.5953], \"unit\": \"N\"}", "dedupe_signature": "e9f324ff36515673ad7a0316da50c7215e14d44776fc4ea077a38a36703b5a6d", "difficulty": "medium", "final_answer": {"answer": [65.9345, 33.5953], "unit": "N"}, "id": "vector_components_005575_74_27", "license": "Apache-2.0", "prompt": "A vector has magnitude 74 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 27, "magnitude": 74.0}, "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. 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=59 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 300.9231, \"unit\": \"m\"}", "dedupe_signature": "4a0299da9ae3e2430f1f4c49b8cc39bdfec94adbfa107d696b181a347de3c185", "difficulty": "medium", "final_answer": {"answer": 300.9231, "unit": "m"}, "id": "projectile_range_005582_59_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59 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=59 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "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. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 45 * 4.61 * 16.\nFinal: {\"answer\": 3319.2, \"unit\": \"J\"}", "dedupe_signature": "d4c4d1cc1eecec66fc81de49ed3fb3618ee3a798db08c39caeae38caba23d357", "difficulty": "easy", "final_answer": {"answer": 3319.2, "unit": "J"}, "id": "heat_q_005602_45_4.61_16", "license": "Apache-2.0", "prompt": "A 45 g sample has specific heat 4.61 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 = 45 * 4.61 * 16.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 4.61, "mass_g": 45}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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 4.5 + 273.15.\nFinal: {\"answer\": 277.65, \"unit\": \"K\"}", "dedupe_signature": "2b33719020c2021a25c7977f36636ef5feadc6f220ad71730e3b8c3bfa51c850", "difficulty": "easy", "final_answer": {"answer": 277.65, "unit": "K"}, "id": "unit_convert_005610_c_to_k_4.5", "license": "Apache-2.0", "prompt": "Convert 4.5 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 4.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 4.5}, "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_005614(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_005614\"}", "dedupe_signature": "18e39cd17610a91632d5ac667c4f8bd256958528d10174f9064bb4f50e78c8fd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_005614"}, "id": "code_005614_finite_differences_005614", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_005614(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": "validation", "task_family": "python_code_generation", "variables": {"function": "finite_differences_005614"}, "verifier": {"function": "finite_differences_005614", "tests": ["assert finite_differences_005614([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_005614([5]) == []", "assert finite_differences_005614([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 40.6^2 and multiply by 0.5 * 4.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3667.601, \"unit\": \"J\"}", "dedupe_signature": "a24c9fea6e58773d41f88e875788eb3cabd2bfc7ad6c67ceb6875cb29361dc17", "difficulty": "easy", "final_answer": {"answer": 3667.601, "unit": "J"}, "id": "ke_005617_4.45_40.6", "license": "Apache-2.0", "prompt": "A body of mass 4.45 kg moves at 40.6 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 = 40.6^2 and multiply by 0.5 * 4.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.45, "velocity": 40.6}, "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 = 240 * 2.69 * 36.\nFinal: {\"answer\": 23241.6, \"unit\": \"J\"}", "dedupe_signature": "c620c8d631c6e46b8332559a18a2a60a1aaa617732f478a5ae8086642210fa49", "difficulty": "easy", "final_answer": {"answer": 23241.6, "unit": "J"}, "id": "heat_q_005620_240_2.69_36", "license": "Apache-2.0", "prompt": "A 240 g sample has specific heat 2.69 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 = 240 * 2.69 * 36.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 36, "heat_capacity": 2.69, "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=100.3 V and R=64.1 ohm.\nFinal: {\"answer\": 156.9437, \"unit\": \"W\"}", "dedupe_signature": "6aa9593c6e08b193417c98333575d0bdce045bdd3d2863a78cc463f17acf7dfa", "difficulty": "easy", "final_answer": {"answer": 156.9437, "unit": "W"}, "id": "ohm_power_005621_100.3_64.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 64.1 ohm and voltage 100.3 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=100.3 V and R=64.1 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 64.1, "voltage": 100.3}, "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) = -0.6 y, so each step multiplies y by 1 - h*0.6.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "a99d03f9720dae3d182d9d0993d6f55446ba41de2109ea50877553b7e484aec0", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_005625_45.5_0.6_1.75_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.6 y with y(0)=45.5, 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) = -0.6 y, so each step multiplies y by 1 - h*0.6.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 45.5, "rate": 0.6, "step": 1.75, "steps": 9}, "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 1441.5 / 100.\nFinal: {\"answer\": 14.415, \"unit\": \"m\"}", "dedupe_signature": "0491e4f766f999e6fd143344ebdd3fca436a35307750e9b01a68d584c31b7360", "difficulty": "easy", "final_answer": {"answer": 14.415, "unit": "m"}, "id": "unit_convert_005628_cm_to_m_1441.5", "license": "Apache-2.0", "prompt": "Convert 1441.5 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 1441.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 1441.5}, "verifier": {"formula": "value / 100", "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 445.5 / 100.\nFinal: {\"answer\": 4.455, \"unit\": \"m\"}", "dedupe_signature": "3617a12d21fa5640c48e7fd592a32df63c1beabba86e8caec90ed590a2062622", "difficulty": "easy", "final_answer": {"answer": 4.455, "unit": "m"}, "id": "unit_convert_005646_cm_to_m_445.5", "license": "Apache-2.0", "prompt": "Convert 445.5 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 445.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 445.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=162 mg, t=5 h, and T_half=30 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 144.3256, \"unit\": \"mg\"}", "dedupe_signature": "78298390891d10465b7a824b31b480492e8304c5ee42b4f48f409187f13f300f", "difficulty": "medium", "final_answer": {"answer": 144.3256, "unit": "mg"}, "id": "half_life_005658_162_30_5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 162 mg. Its half-life is 30 hours. How many mg remain after 5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=162 mg, t=5 h, and T_half=30 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 5.0, "half_life": 30.0, "initial_amount": 162.0}, "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) = -0.48 y, so each step multiplies y by 1 - h*0.48.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0012, \"unit\": \"state_units\"}", "dedupe_signature": "1032cd7b7caea1ff2b1fff19bf44e0d20e19e007a14d22aaa0d54b601b7ba4ca", "difficulty": "medium", "final_answer": {"answer": 0.0012, "unit": "state_units"}, "id": "euler_decay_005661_35_0.48_1.2_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.48 y with y(0)=35, step size h=1.2, 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) = -0.48 y, so each step multiplies y by 1 - h*0.48.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.48, "step": 1.2, "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. 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": "6a514ac0a0cc44135e3073f682570b70c93e248dd3b6dd982b0cf6d333983fc7", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005667_consistent_4153435f_500916", "license": "Apache-2.0", "prompt": "In lab notebook case 500916, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 295 * 4.365 * 52.\nFinal: {\"answer\": 66959.1, \"unit\": \"J\"}", "dedupe_signature": "7562d4958f7c058e50dc9cfec57d6bcad505b916e5db6e57c4c6dcfdf25cf664", "difficulty": "easy", "final_answer": {"answer": 66959.1, "unit": "J"}, "id": "heat_q_005674_295_4.365_52", "license": "Apache-2.0", "prompt": "A 295 g sample has specific heat 4.365 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 = 295 * 4.365 * 52.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 52, "heat_capacity": 4.365, "mass_g": 295}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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": "7db2b75159e336e086971e468880beebb419c6115816570d8620ffe36b0057c1", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005687_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.54 mol and T=480 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": "validation", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_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": "2160733316ca9cc550465bec638b068d5958f9b7dc1a5e0e5f0958e29deb401c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005705_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 4801 items and budget 99085, 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": "validation", "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. Mass equals amount in moles times molar mass.\n2. Use m = 1.89 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 340.4948, \"unit\": \"g\"}", "dedupe_signature": "b497caa3cbb6611f0cacd278e492204c393b4f4dff3b166c45515c7bc7794dd4", "difficulty": "medium", "final_answer": {"answer": 340.4948, "unit": "g"}, "id": "stoich_mass_005713_glucose_1.89", "license": "Apache-2.0", "prompt": "A sample contains 1.89 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 = 1.89 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.89}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.75^2 and multiply by 0.5 * 17.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 15556.8328, \"unit\": \"J\"}", "dedupe_signature": "3f8ee4d0a86f40a9d00d55779cdb01f671de232c492f4bcc67795e778d020ce6", "difficulty": "easy", "final_answer": {"answer": 15556.8328, "unit": "J"}, "id": "ke_005743_17.85_41.75", "license": "Apache-2.0", "prompt": "A body of mass 17.85 kg moves at 41.75 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 = 41.75^2 and multiply by 0.5 * 17.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.85, "velocity": 41.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4245 mL to 4.245 L.\n3. Compute M = 2.485 / 4.245.\nFinal: {\"answer\": 0.5854, \"unit\": \"mol/L\"}", "dedupe_signature": "521d5bd826501588fcf80df73d4a6066c24d1d4bd6bc0f3486f32d6d2cb685f2", "difficulty": "medium", "final_answer": {"answer": 0.5854, "unit": "mol/L"}, "id": "molarity_005750_2.485_4245", "license": "Apache-2.0", "prompt": "A solution contains 2.485 mol of solute in 4245 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4245 mL to 4.245 L.\nCompute M = 2.485 / 4.245.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.485, "volume_ml": 4245}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.5^2 and multiply by 0.5 * 4.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4470.4688, \"unit\": \"J\"}", "dedupe_signature": "0cef353372b4b78bb45439c588fb1d034e4613988626a3f4c73264bec5da76d9", "difficulty": "easy", "final_answer": {"answer": 4470.4688, "unit": "J"}, "id": "ke_005761_4.95_42.5", "license": "Apache-2.0", "prompt": "A body of mass 4.95 kg moves at 42.5 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 = 42.5^2 and multiply by 0.5 * 4.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.95, "velocity": 42.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4215 mL to 4.215 L.\n3. Compute M = 2.81 / 4.215.\nFinal: {\"answer\": 0.6667, \"unit\": \"mol/L\"}", "dedupe_signature": "1c6a7b3a1cdff8949ece8b299b5ac14c7e3310ee738a08657a253938ce5b668e", "difficulty": "medium", "final_answer": {"answer": 0.6667, "unit": "mol/L"}, "id": "molarity_005768_2.81_4215", "license": "Apache-2.0", "prompt": "A solution contains 2.81 mol of solute in 4215 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4215 mL to 4.215 L.\nCompute M = 2.81 / 4.215.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.81, "volume_ml": 4215}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.82 * 8.314 * 589 / 31.5.\nFinal: {\"answer\": 127.4761, \"unit\": \"kPa\"}", "dedupe_signature": "b74de209723f977fafb2df440f90aec51aa2d933ca41c360925bac7991a110d3", "difficulty": "medium", "final_answer": {"answer": 127.4761, "unit": "kPa"}, "id": "ideal_gas_005781_0.82_589_31.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.82 mol, T=589 K, and V=31.5 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 = 0.82 * 8.314 * 589 / 31.5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.82, "temp_k": 589, "volume_l": 31.5}, "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=148.7 V and R=119.4 ohm.\nFinal: {\"answer\": 185.19, \"unit\": \"W\"}", "dedupe_signature": "9fe5b23b7e6555a3247b3675adf8218865697a60a7f283af06066e2817bcc629", "difficulty": "easy", "final_answer": {"answer": 185.19, "unit": "W"}, "id": "ohm_power_005783_148.7_119.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 119.4 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=119.4 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 119.4, "voltage": 148.7}, "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(8.7)=19.53 and f(13.1)=23.49.\n3. The interval width is 4.4.\nFinal: {\"answer\": 94.644, \"unit\": \"area_units\"}", "dedupe_signature": "239fbc5a39a905bb5d847c06bc8fd386fec1724e21fc42a97590d8d846fa3899", "difficulty": "medium", "final_answer": {"answer": 94.644, "unit": "area_units"}, "id": "trapz_linear_005788_0.9_11.7_8.7_13.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.9x+11.7 from x=8.7 to x=13.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.7)=19.53 and f(13.1)=23.49.\nThe interval width is 4.4.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 11.7, "slope": 0.9, "x0": 8.7, "x1": 13.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_005794(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_005794\"}", "dedupe_signature": "268cbfeb8175c772be834ad5eb3fb48e03cc74a65b0ef6f772511973c8e19eec", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005794"}, "id": "code_005794_clamp_005794", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005794(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": "validation", "task_family": "python_code_generation", "variables": {"function": "clamp_005794"}, "verifier": {"function": "clamp_005794", "tests": ["assert clamp_005794(5, 0, 10) == 5", "assert clamp_005794(-2, 0, 10) == 0", "assert clamp_005794(12, 0, 10) == 10", "try:\n    clamp_005794(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1020 * 1.625 * 46.\nFinal: {\"answer\": 76245.0, \"unit\": \"J\"}", "dedupe_signature": "69fc064ce992ca6a52d7ba24cca85b76701f5445bc08ca416311fe5605d050cd", "difficulty": "easy", "final_answer": {"answer": 76245.0, "unit": "J"}, "id": "heat_q_005800_1020_1.625_46", "license": "Apache-2.0", "prompt": "A 1020 g sample has specific heat 1.625 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 = 1020 * 1.625 * 46.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 46, "heat_capacity": 1.625, "mass_g": 1020}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "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=44.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 143.2549, \"unit\": \"m\"}", "dedupe_signature": "e27c085cf6a382bcda8b86891df5be1093c755715386644bfbd9a2d8338b357e", "difficulty": "medium", "final_answer": {"answer": 143.2549, "unit": "m"}, "id": "projectile_range_005816_44.2_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 44.2 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=44.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 44.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 750 mL to 0.75 L.\n3. Compute M = 2.425 / 0.75.\nFinal: {\"answer\": 3.2333, \"unit\": \"mol/L\"}", "dedupe_signature": "05ed735a5727530af87695ec9e3aa473a5f2436fd6c18568f0eb11bb121ea43e", "difficulty": "medium", "final_answer": {"answer": 3.2333, "unit": "mol/L"}, "id": "molarity_005822_2.425_750", "license": "Apache-2.0", "prompt": "A solution contains 2.425 mol of solute in 750 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 750 mL to 0.75 L.\nCompute M = 2.425 / 0.75.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 2.425, "volume_ml": 750}, "verifier": {"formula": "moles / (volume_ml / 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=80 degrees and keep the unit as newtons.\nFinal: {\"answer\": [1.1287, 6.4013], \"unit\": \"N\"}", "dedupe_signature": "00a0df232e96f0e2432eed1d132c6c469998f55d039c61d277a1c5c8253bab50", "difficulty": "medium", "final_answer": {"answer": [1.1287, 6.4013], "unit": "N"}, "id": "vector_components_005827_6.5_80", "license": "Apache-2.0", "prompt": "A vector has magnitude 6.5 N at 80 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=80 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 80, "magnitude": 6.5}, "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. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 500 * 1.555 * 110.\nFinal: {\"answer\": 85525.0, \"unit\": \"J\"}", "dedupe_signature": "c05b027281c0cf6a1a093266653963c16c31649161c6b7c94294e12d8eed9032", "difficulty": "easy", "final_answer": {"answer": 85525.0, "unit": "J"}, "id": "heat_q_005836_500_1.555_110", "license": "Apache-2.0", "prompt": "A 500 g sample has specific heat 1.555 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 = 500 * 1.555 * 110.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 110, "heat_capacity": 1.555, "mass_g": 500}, "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 2770 mL to 2.77 L.\n3. Compute M = 3.515 / 2.77.\nFinal: {\"answer\": 1.269, \"unit\": \"mol/L\"}", "dedupe_signature": "14ace811092ed796bff20a773b6bc559b861340de1fc2efe0040eab6b0ed6e9a", "difficulty": "medium", "final_answer": {"answer": 1.269, "unit": "mol/L"}, "id": "molarity_005840_3.515_2770", "license": "Apache-2.0", "prompt": "A solution contains 3.515 mol of solute in 2770 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2770 mL to 2.77 L.\nCompute M = 3.515 / 2.77.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 3.515, "volume_ml": 2770}, "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=0.22 and add it to the current value.\nFinal: {\"answer\": [1.384, 0.876, 0.921], \"unit\": \"temperature_units\"}", "dedupe_signature": "332f53cabb1d55746815f47ae56c07b5135818657966a67611a8db61d9565465", "difficulty": "hard", "final_answer": {"answer": [1.384, 0.876, 0.921], "unit": "temperature_units"}, "id": "heat_step_005843_0.22_0.2_2.55_-0.4_2.45_-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=0.2, right=-1.65; current interior values are [2.55, -0.4, 2.45]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.55, -0.4, 2.45], "left": 0.2, "r": 0.22, "right": -1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_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": "ccd000cab849b5faa6ca5e4d9aad6a70665f345cd3f861ed9a90d5ed87326fc5", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_005849_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 60.2 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": "validation", "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. 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": "6a9bf4ab07c8051612b5b1b91b02acd243b981a6573873e217b3e42375388d2a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005865_inconsistent_c1271127_886821", "license": "Apache-2.0", "prompt": "In sensor calibration case 886821, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = 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=69 degrees through the sine of 2 theta.\n3. Substitute v=46.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 145.5881, \"unit\": \"m\"}", "dedupe_signature": "653d6fab3459587eeea5cfb141463353ffb6cf9be20df8408ff5c84c1280773e", "difficulty": "medium", "final_answer": {"answer": 145.5881, "unit": "m"}, "id": "projectile_range_005888_46.2_69", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 46.2 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=46.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 69, "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 = 1.64 * 8.314 * 253 / 53.4.\nFinal: {\"answer\": 64.6001, \"unit\": \"kPa\"}", "dedupe_signature": "179152212b994228885f6770d4a31565049a71f2621340df7f46201642e90e8f", "difficulty": "medium", "final_answer": {"answer": 64.6001, "unit": "kPa"}, "id": "ideal_gas_005889_1.64_253_53.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.64 mol, T=253 K, and V=53.4 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 = 1.64 * 8.314 * 253 / 53.4.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 1.64, "temp_k": 253, "volume_l": 53.4}, "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 = 1340 * 4.615 * 12.\nFinal: {\"answer\": 74209.2, \"unit\": \"J\"}", "dedupe_signature": "723feb22aa391263fcac675b4e2f3f2be59baea790a6173d3d00874c4cff33d7", "difficulty": "easy", "final_answer": {"answer": 74209.2, "unit": "J"}, "id": "heat_q_005890_1340_4.615_12", "license": "Apache-2.0", "prompt": "A 1340 g sample has specific heat 4.615 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 = 1340 * 4.615 * 12.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 12, "heat_capacity": 4.615, "mass_g": 1340}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.963, 1.096, 0.205], \"unit\": \"temperature_units\"}", "dedupe_signature": "b8f28802e9447ee41c8fe551f880de968e85a3d8a6fc314fe90f15e22797e903", "difficulty": "hard", "final_answer": {"answer": [-0.963, 1.096, 0.205], "unit": "temperature_units"}, "id": "heat_step_005897_0.46_-1.2_2.05_-1.25_0.55_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=-1.2, right=1.6; current interior values are [2.05, -1.25, 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.05, -1.25, 0.55], "left": -1.2, "r": 0.46, "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. 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": "913ba8310ad2191c109d95d73e86ffa4e29c3df6cdac6b241efc1b8af9ca5456", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005901_consistent_b7d3eed1_259012", "license": "Apache-2.0", "prompt": "In simulation spec case 259012, 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": "validation", "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: 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": "a853938c5b840b9cfe68607bc2f681a5ad6bbf865c563f98c00c49366213485c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_005903_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse ledger records in release 840086, 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": "validation", "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. The function contract has a 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_005920(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_005920\"}", "dedupe_signature": "6c370943358007ecd25d31c80221ee0d15875b82b6856b699371fadc9e578529", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_005920"}, "id": "code_005920_center_values_005920", "license": "Apache-2.0", "prompt": "Write a Python function center_values_005920(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": "validation", "task_family": "python_code_generation", "variables": {"function": "center_values_005920"}, "verifier": {"function": "center_values_005920", "tests": ["out = center_values_005920([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_005920([5]) == [0]", "try:\n    center_values_005920([])\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 = 14 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 141.4, \"unit\": \"N\"}", "dedupe_signature": "f34783b624e063eea5fdead7a5369e0992ca5bc00ebc89f26eca255a590f200d", "difficulty": "easy", "final_answer": {"answer": 141.4, "unit": "N"}, "id": "force_005922_10.1_14", "license": "Apache-2.0", "prompt": "A cart has mass 10.1 kg and measured acceleration 14 m/s^2. Compute the net force. 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 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.0, "mass": 10.1}, "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=159.5 V and R=190.3 ohm.\nFinal: {\"answer\": 133.685, \"unit\": \"W\"}", "dedupe_signature": "f670cf5a6a910c95bb3a3af8bda18dc997962a2eaf7a653be38c679ed42a6c45", "difficulty": "easy", "final_answer": {"answer": 133.685, "unit": "W"}, "id": "ohm_power_005927_159.5_190.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 190.3 ohm and voltage 159.5 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=159.5 V and R=190.3 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 190.3, "voltage": 159.5}, "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 = 2.03 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 203.1766, \"unit\": \"g\"}", "dedupe_signature": "56baf163084768112495dde8cceb7c030691506f4d95f5c6a23469f891e168f7", "difficulty": "medium", "final_answer": {"answer": 203.1766, "unit": "g"}, "id": "stoich_mass_005929_calcium_carbonate_2.03", "license": "Apache-2.0", "prompt": "A sample contains 2.03 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 = 2.03 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.03}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 16.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "14fc5fae6fbb34eadb358abb82770d6e04ec344396480304b0ef5ee973749ee4", "difficulty": "medium", "final_answer": {"answer": [5.55, 16.0], "unit": "dimensionless"}, "id": "line_two_point_005936_5.25_16_5.55_16", "license": "Apache-2.0", "prompt": "A line passes through points (5.25, 45.1375) and (16, 104.8). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 5.25, "x2": 16.0, "y1": 45.1375, "y2": 104.8}, "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. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "dbd99fe12efd2720629758f9547d98658886e7f4cf7a3d2db6d2fef3643fe005", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005937_consistent_03f5e041_698779", "license": "Apache-2.0", "prompt": "In student derivation case 698779, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "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 = 4.48 * 8.314 * 440 / 7.8.\nFinal: {\"answer\": 2101.097, \"unit\": \"kPa\"}", "dedupe_signature": "5648859b3feb598a480f53f132ae36590b130bf49581683d51b01c64a80adc50", "difficulty": "medium", "final_answer": {"answer": 2101.097, "unit": "kPa"}, "id": "ideal_gas_005943_4.48_440_7.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.48 mol, T=440 K, and V=7.8 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 * 440 / 7.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.48, "temp_k": 440, "volume_l": 7.8}, "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=604.5 mg, t=193 h, and T_half=37 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 16.2614, \"unit\": \"mg\"}", "dedupe_signature": "9fd7a43a05824c819d69716700ee8235143a5f384943f6641ec32ec4e517eb77", "difficulty": "medium", "final_answer": {"answer": 16.2614, "unit": "mg"}, "id": "half_life_005946_604.5_37_193", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 604.5 mg. Its half-life is 37 hours. How many mg remain after 193 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=604.5 mg, t=193 h, and T_half=37 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 193.0, "half_life": 37.0, "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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.6)=4.14 and f(1.6)=-10.74.\n3. The interval width is 6.2.\nFinal: {\"answer\": -20.46, \"unit\": \"area_units\"}", "dedupe_signature": "d066d0a2006c98356c1f2d99beecd7203bdc9168d67d4417ebcba19f7f1307f6", "difficulty": "medium", "final_answer": {"answer": -20.46, "unit": "area_units"}, "id": "trapz_linear_005950_-2.4_-6.9_-4.6_1.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.4x+-6.9 from x=-4.6 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(-4.6)=4.14 and f(1.6)=-10.74.\nThe interval width is 6.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -6.9, "slope": -2.4, "x0": -4.6, "x1": 1.6000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.45^2 and multiply by 0.5 * 15.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1019.3219, \"unit\": \"J\"}", "dedupe_signature": "fa2d5c075dee7929c0f72b41283723b3289885327d54cb8d9d5c7b10a5949c9f", "difficulty": "easy", "final_answer": {"answer": 1019.3219, "unit": "J"}, "id": "ke_005959_15.55_11.45", "license": "Apache-2.0", "prompt": "A body of mass 15.55 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 * 15.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.55, "velocity": 11.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"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 2 steps and round the final state.\nFinal: {\"answer\": 6.3315, \"unit\": \"state_units\"}", "dedupe_signature": "23500943c87d221716b2e9789194312358200bd6267b3e57675f20f1cc9b260a", "difficulty": "medium", "final_answer": {"answer": 6.3315, "unit": "state_units"}, "id": "euler_decay_005985_11.5_0.86_0.3_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.86 y with y(0)=11.5, 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) = -0.86 y, so each step multiplies y by 1 - h*0.86.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 11.5, "rate": 0.86, "step": 0.3, "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=0.26 and add it to the current value.\nFinal: {\"answer\": [1.397, 2.241, 1.888], \"unit\": \"temperature_units\"}", "dedupe_signature": "973382c596a9cb679b297b75dc1362bd66987d119203967d6183d7c105b98617", "difficulty": "hard", "final_answer": {"answer": [1.397, 2.241, 1.888], "unit": "temperature_units"}, "id": "heat_step_005987_0.26_-0.1_1.8_2.15_2.85_-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=-0.1, right=-0.15; current interior values are [1.8, 2.15, 2.85]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.8, 2.15, 2.85], "left": -0.1, "r": 0.26, "right": -0.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R 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 * 8.314 * 414 / 14.1.\nFinal: {\"answer\": 488.2264, \"unit\": \"kPa\"}", "dedupe_signature": "70294b7535158e77dc9fae191a911773225a7abca025bf33b30970f50e337813", "difficulty": "medium", "final_answer": {"answer": 488.2264, "unit": "kPa"}, "id": "ideal_gas_005997_2_414_14.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2 mol, T=414 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 * 8.314 * 414 / 14.1.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.0, "temp_k": 414, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=519 mg, t=160.5 h, and T_half=108 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 185.2692, \"unit\": \"mg\"}", "dedupe_signature": "5d9a2691a31522303662c105c36ae16012e2b8382697227fab9b5bef90af7788", "difficulty": "medium", "final_answer": {"answer": 185.2692, "unit": "mg"}, "id": "half_life_006000_519_108_160.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 519 mg. Its half-life is 108 hours. How many mg remain after 160.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=519 mg, t=160.5 h, and T_half=108 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 160.5, "half_life": 108.0, "initial_amount": 519.0}, "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 * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 17.4746, \"unit\": \"g\"}", "dedupe_signature": "79f7ac6e604de5f22470fb6e894ac2bdba4e2401a78663b7791d64aaded3ccf6", "difficulty": "medium", "final_answer": {"answer": 17.4746, "unit": "g"}, "id": "stoich_mass_006001_water_0.97", "license": "Apache-2.0", "prompt": "A sample contains 0.97 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 = 0.97 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.97}, "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=0.28 and add it to the current value.\nFinal: {\"answer\": [0.884, 1.068, 0.966], \"unit\": \"temperature_units\"}", "dedupe_signature": "4f5df816d6bebabe7f0407e36384b434609bd34649e08af41b23725e83a8f7ba", "difficulty": "hard", "final_answer": {"answer": [0.884, 1.068, 0.966], "unit": "temperature_units"}, "id": "heat_step_006005_0.28_-0.45_1.5_1.25_0.35_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=-0.45, right=1.65; current interior values are [1.5, 1.25, 0.35]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, 1.25, 0.35], "left": -0.45, "r": 0.28, "right": 1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_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 * 0.8 * 115.\nFinal: {\"answer\": 178480.0, \"unit\": \"J\"}", "dedupe_signature": "f9ecc0eef26dcfeadc0a307a82b275b4a6b16960bac64036a81ea623d56665bf", "difficulty": "easy", "final_answer": {"answer": 178480.0, "unit": "J"}, "id": "heat_q_006016_1940_0.8_115", "license": "Apache-2.0", "prompt": "A 1940 g sample has specific heat 0.8 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 = 1940 * 0.8 * 115.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 0.8, "mass_g": 1940}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "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=47.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 220.3531, \"unit\": \"m\"}", "dedupe_signature": "9f343e5ee14e50f7a9b2b9f1a9caaba42842e8775eb4469d04f970a2cec7c9ff", "difficulty": "medium", "final_answer": {"answer": 220.3531, "unit": "m"}, "id": "projectile_range_006032_47.2_52", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 47.2 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=47.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 52, "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. 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, 1.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "cb6f69a28d84c4dcdef5bab1c3151e0d904a91579c9a9ba02714bf931589234f", "difficulty": "medium", "final_answer": {"answer": [-9.2, 1.0], "unit": "dimensionless"}, "id": "line_two_point_006044_-7_1.75_-9.2_1", "license": "Apache-2.0", "prompt": "A line passes through points (-7, 65.4) and (1.75, -15.1). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -7.0, "x2": 1.75, "y1": 65.39999999999999, "y2": -15.099999999999998}, "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 = 6.85^2 and multiply by 0.5 * 4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 93.845, \"unit\": \"J\"}", "dedupe_signature": "df7f5e47a5c1ff68792baedcb6e34b8c0e8617ac410c72a7b6f513ba9a2705c7", "difficulty": "easy", "final_answer": {"answer": 93.845, "unit": "J"}, "id": "ke_006049_4_6.85", "license": "Apache-2.0", "prompt": "A body of mass 4 kg moves at 6.85 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 = 6.85^2 and multiply by 0.5 * 4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.0, "velocity": 6.85}, "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=897.5 mg, t=161.5 h, and T_half=20 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.3283, \"unit\": \"mg\"}", "dedupe_signature": "1390e7240e1514699cb16389d80c41455f27b2491a205ec13eca1d0c2296a3b1", "difficulty": "medium", "final_answer": {"answer": 3.3283, "unit": "mg"}, "id": "half_life_006090_897.5_20_161.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 897.5 mg. Its half-life is 20 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=897.5 mg, t=161.5 h, and T_half=20 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 161.5, "half_life": 20.0, "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. The function contract has a 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_006100(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_006100\"}", "dedupe_signature": "27cd311ab1eb60d08ee825f8f722df4f3f107480a0db2b22d6fb7fa8abb54e12", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_006100"}, "id": "code_006100_clamp_006100", "license": "Apache-2.0", "prompt": "Write a Python function clamp_006100(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": "validation", "task_family": "python_code_generation", "variables": {"function": "clamp_006100"}, "verifier": {"function": "clamp_006100", "tests": ["assert clamp_006100(5, 0, 10) == 5", "assert clamp_006100(-2, 0, 10) == 0", "assert clamp_006100(12, 0, 10) == 10", "try:\n    clamp_006100(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 = 21.2^2 and multiply by 0.5 * 15.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3382.036, \"unit\": \"J\"}", "dedupe_signature": "54c1a5abc7aed11d438f273a7ae08a6d926f4fb8ed3b606042cd3191a0080654", "difficulty": "easy", "final_answer": {"answer": 3382.036, "unit": "J"}, "id": "ke_006103_15.05_21.2", "license": "Apache-2.0", "prompt": "A body of mass 15.05 kg moves at 21.2 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 = 21.2^2 and multiply by 0.5 * 15.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.05, "velocity": 21.2}, "verifier": {"formula": "0.5 * mass * velocity ** 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=34 degrees and keep the unit as newtons.\nFinal: {\"answer\": [32.747, 22.0881], \"unit\": \"N\"}", "dedupe_signature": "8e279c9ed3954c807e4653970604b0c67a63227fab3c3598912155484e169344", "difficulty": "medium", "final_answer": {"answer": [32.747, 22.0881], "unit": "N"}, "id": "vector_components_006133_39.5_34", "license": "Apache-2.0", "prompt": "A vector has magnitude 39.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 34, "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. Use Newton's second law F = m a.\n2. Substitute m = 5.3 kg and a = 14.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 76.85, \"unit\": \"N\"}", "dedupe_signature": "73c2401c5199315cbd61a40850a278a12ab6816e98368f7b536fa2ed0139fc47", "difficulty": "easy", "final_answer": {"answer": 76.85, "unit": "N"}, "id": "force_006138_5.3_14.5", "license": "Apache-2.0", "prompt": "A cart has mass 5.3 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 = 5.3 kg and a = 14.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.5, "mass": 5.3}, "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 = 4.78 * 8.314 * 259 / 40.0.\nFinal: {\"answer\": 257.3225, \"unit\": \"kPa\"}", "dedupe_signature": "f60170ba38f2b8f8feb36cad4a1937bd2e6fa7200a88d6ee05bbb6929cdf55cb", "difficulty": "medium", "final_answer": {"answer": 257.3225, "unit": "kPa"}, "id": "ideal_gas_006141_4.78_259_40.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.78 mol, T=259 K, and V=40.0 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 = 4.78 * 8.314 * 259 / 40.0.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.78, "temp_k": 259, "volume_l": 40.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 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 * 9.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 31.6997, \"unit\": \"J\"}", "dedupe_signature": "158a5195bb8c6495cb5612a8633557893012b1f1c2de81de91f9561a8f7f71e5", "difficulty": "easy", "final_answer": {"answer": 31.6997, "unit": "J"}, "id": "ke_006157_9.75_2.55", "license": "Apache-2.0", "prompt": "A body of mass 9.75 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 * 9.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.75, "velocity": 2.55}, "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 = 1595 * 2.84 * 59.\nFinal: {\"answer\": 267258.2, \"unit\": \"J\"}", "dedupe_signature": "9c821f12feb7352888a75cdb59c59a261657f6401c359e89adab8a0d3e589fe1", "difficulty": "easy", "final_answer": {"answer": 267258.2, "unit": "J"}, "id": "heat_q_006160_1595_2.84_59", "license": "Apache-2.0", "prompt": "A 1595 g sample has specific heat 2.84 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 = 1595 * 2.84 * 59.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 59, "heat_capacity": 2.84, "mass_g": 1595}, "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=217.5 mg, t=179 h, and T_half=60 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 27.5034, \"unit\": \"mg\"}", "dedupe_signature": "0075e87ae4731da52ba45150f69db1610abb2e68e7c1fdefb14adeb0f7a25604", "difficulty": "medium", "final_answer": {"answer": 27.5034, "unit": "mg"}, "id": "half_life_006162_217.5_60_179", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 217.5 mg. Its half-life is 60 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=217.5 mg, t=179 h, and T_half=60 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 179.0, "half_life": 60.0, "initial_amount": 217.5}, "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 9 steps and round the final state.\nFinal: {\"answer\": 23.5184, \"unit\": \"state_units\"}", "dedupe_signature": "1acec2ab3a745fd36d9dd866193645f64ba6823adbfce5f7bf3c748f8bc43985", "difficulty": "medium", "final_answer": {"answer": 23.5184, "unit": "state_units"}, "id": "euler_decay_006183_68.5_0.14_0.8_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.14 y with y(0)=68.5, step size h=0.8, 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) = -0.14 y, so each step multiplies y by 1 - h*0.14.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 68.5, "rate": 0.14, "step": 0.8, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=304 degrees and keep the unit as newtons.\nFinal: {\"answer\": [137.0023, -203.1142], \"unit\": \"N\"}", "dedupe_signature": "3865d56757565a9e272bfa937f26d08c97d1b34a52b0f3c22f130eb1439cf6cb", "difficulty": "medium", "final_answer": {"answer": [137.0023, -203.1142], "unit": "N"}, "id": "vector_components_006205_245_304", "license": "Apache-2.0", "prompt": "A vector has magnitude 245 N at 304 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=304 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 304, "magnitude": 245.0}, "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. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 750 * 3.49 * 18.\nFinal: {\"answer\": 47115.0, \"unit\": \"J\"}", "dedupe_signature": "147f0b2dc1ed5d4c4dcf2e388b3399bebabbebd75ce65736d4cc6f235089d264", "difficulty": "easy", "final_answer": {"answer": 47115.0, "unit": "J"}, "id": "heat_q_006214_750_3.49_18", "license": "Apache-2.0", "prompt": "A 750 g sample has specific heat 3.49 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 = 750 * 3.49 * 18.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 18, "heat_capacity": 3.49, "mass_g": 750}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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)=4.72 and f(11.4)=6.56.\n3. The interval width is 4.6.\nFinal: {\"answer\": 25.944, \"unit\": \"area_units\"}", "dedupe_signature": "8dd6e8568fac7a6b4d89470032a780b906b88171dbc4f556932dfd0a613eb662", "difficulty": "medium", "final_answer": {"answer": 25.944, "unit": "area_units"}, "id": "trapz_linear_006220_0.4_2_6.8_11.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.4x+2 from x=6.8 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(6.8)=4.72 and f(11.4)=6.56.\nThe interval width is 4.6.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 2.0, "slope": 0.4, "x0": 6.8, "x1": 11.399999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 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 * 519 / 114.7.\nFinal: {\"answer\": 188.8503, \"unit\": \"kPa\"}", "dedupe_signature": "9c94f9532308c148fccb2abdcc0ce123fa7c9aaa40b85a89c0f57eb7a27a2396", "difficulty": "medium", "final_answer": {"answer": 188.8503, "unit": "kPa"}, "id": "ideal_gas_006231_5.02_519_114.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.02 mol, T=519 K, and V=114.7 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 = 5.02 * 8.314 * 519 / 114.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 5.02, "temp_k": 519, "volume_l": 114.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.814, 2.183, 1.24], \"unit\": \"temperature_units\"}", "dedupe_signature": "0522c2863ab5a28b9baa9b1b4bdebd90a20849a379b385c238e7e3c32e4caa66", "difficulty": "hard", "final_answer": {"answer": [1.814, 2.183, 1.24], "unit": "temperature_units"}, "id": "heat_step_006239_0.26_1.35_1.45_2.95_1.5_-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 [1.45, 2.95, 1.5]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.45, 2.95, 1.5], "left": 1.35, "r": 0.26, "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=293 degrees and keep the unit as newtons.\nFinal: {\"answer\": [149.8454, -353.0136], \"unit\": \"N\"}", "dedupe_signature": "f75374d7afda4ce941cce17b8603d65e2bdab72c5f003c4e728066b04d35afb1", "difficulty": "medium", "final_answer": {"answer": [149.8454, -353.0136], "unit": "N"}, "id": "vector_components_006241_383.5_293", "license": "Apache-2.0", "prompt": "A vector has magnitude 383.5 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 293, "magnitude": 383.5}, "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": "ef71abe61e05ee98b2f69442ae667d4d55a4ab398970bfff985072115f552218", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006245_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=51 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": "validation", "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 = 5.7^2 and multiply by 0.5 * 19.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 315.9653, \"unit\": \"J\"}", "dedupe_signature": "7055df67457d841e9a0d82fb2b023feeb8176d6d3d93650c34a3894e84b3972e", "difficulty": "easy", "final_answer": {"answer": 315.9653, "unit": "J"}, "id": "ke_006247_19.45_5.7", "license": "Apache-2.0", "prompt": "A body of mass 19.45 kg moves at 5.7 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 = 5.7^2 and multiply by 0.5 * 19.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.45, "velocity": 5.7}, "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=22 degrees through the sine of 2 theta.\n3. Substitute v=12 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 10.1968, \"unit\": \"m\"}", "dedupe_signature": "f749dbb09d90d93fef6743c466bebed8f8b7b7d19d2481af548e72a51ed9474c", "difficulty": "medium", "final_answer": {"answer": 10.1968, "unit": "m"}, "id": "projectile_range_006266_12_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 12 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=12 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "gravity": 9.81, "speed": 12.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "053852913a17b88b6d8d84c4604b3738b7bc0f02e06c727e4c52065b897bf040", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006281_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=1 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": "validation", "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 Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1760 * 0.865 * 39.\nFinal: {\"answer\": 59373.6, \"unit\": \"J\"}", "dedupe_signature": "cef48b4938441f03c99cc599cdc904eaeb2790fd965acf6f3690fb9632b27f28", "difficulty": "easy", "final_answer": {"answer": 59373.6, "unit": "J"}, "id": "heat_q_006286_1760_0.865_39", "license": "Apache-2.0", "prompt": "A 1760 g sample has specific heat 0.865 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 = 1760 * 0.865 * 39.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 39, "heat_capacity": 0.865, "mass_g": 1760}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [-205.8248, 36.2925], \"unit\": \"N\"}", "dedupe_signature": "25ba0cc38c756a8ddf0031f439d090b12262a58b43c8c4faa35f06db140699b9", "difficulty": "medium", "final_answer": {"answer": [-205.8248, 36.2925], "unit": "N"}, "id": "vector_components_006313_209_170", "license": "Apache-2.0", "prompt": "A vector has magnitude 209 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 170, "magnitude": 209.0}, "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\": [7.2, 18.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "b25cbf9184c30290f971edcaaeb85efa4b32bd57c6069e738d897e22257cd37f", "difficulty": "medium", "final_answer": {"answer": [7.2, 18.0], "unit": "dimensionless"}, "id": "line_two_point_006314_-16.75_-11.75_7.2_18", "license": "Apache-2.0", "prompt": "A line passes through points (-16.75, -102.6) and (-11.75, -66.6). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -16.75, "x2": -11.75, "y1": -102.60000000000001, "y2": -66.60000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - 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": "849332859218f32fea5db9627470109b953290c51e0f22284cbe3437aacc2e29", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006315_consistent_5ca82cb9_665696", "license": "Apache-2.0", "prompt": "In simulation spec case 665696, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"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 148.0 + 273.15.\nFinal: {\"answer\": 421.15, \"unit\": \"K\"}", "dedupe_signature": "678ce3e9d8d65d6bc9c5107b6a34409bc3040218e8242e3eb85d9c3cf57de421", "difficulty": "easy", "final_answer": {"answer": 421.15, "unit": "K"}, "id": "unit_convert_006348_c_to_k_148", "license": "Apache-2.0", "prompt": "Convert 148 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 148.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 148.0}, "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. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "bb90ffe689de940e6269261d7d72911b284eeb0c078c4ad257ffd238fa16c3ff", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006351_inconsistent_74ac0b02_681836", "license": "Apache-2.0", "prompt": "In simulation spec case 681836, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=700.5 mg, t=198.5 h, and T_half=82.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 132.1636, \"unit\": \"mg\"}", "dedupe_signature": "265e9a1853b0dc3d8687ff8e37e3681d791c222d9bdabb8bc2ea2a24e899872f", "difficulty": "medium", "final_answer": {"answer": 132.1636, "unit": "mg"}, "id": "half_life_006360_700.5_82.5_198.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 700.5 mg. Its half-life is 82.5 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=700.5 mg, t=198.5 h, and T_half=82.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 198.5, "half_life": 82.5, "initial_amount": 700.5}, "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(8.2)=-63.44 and f(15.9)=-111.18.\n3. The interval width is 7.7.\nFinal: {\"answer\": -672.287, \"unit\": \"area_units\"}", "dedupe_signature": "a5a813ef4e8ac607ae5f5282496d893718de45e0085ebeaacd5b97cde221c9c9", "difficulty": "medium", "final_answer": {"answer": -672.287, "unit": "area_units"}, "id": "trapz_linear_006364_-6.2_-12.6_8.2_15.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.2x+-12.6 from x=8.2 to x=15.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.2)=-63.44 and f(15.9)=-111.18.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -12.6, "slope": -6.2, "x0": 8.2, "x1": 15.899999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "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=11.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 7.2687, \"unit\": \"m\"}", "dedupe_signature": "2e6558d167771b5cd9fe522d82954e161176672b8e5e8d107b7562bc0605156d", "difficulty": "medium", "final_answer": {"answer": 7.2687, "unit": "m"}, "id": "projectile_range_006392_11.6_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.6 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=11.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "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. 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=146.8 ohm.\nFinal: {\"answer\": 200.8235, \"unit\": \"W\"}", "dedupe_signature": "61c5c59d2ff1572fca2c2b43f165fbf2fde5c2d4f9d5cecac7ffb9a325004c80", "difficulty": "easy", "final_answer": {"answer": 200.8235, "unit": "W"}, "id": "ohm_power_006395_171.7_146.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 146.8 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=146.8 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 146.8, "voltage": 171.7}, "verifier": {"formula": "voltage ** 2 / resistance", "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_006406(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_006406\"}", "dedupe_signature": "6a43aa44f33a5837c4bf308b06b803aaa2b797c2ebdb58e9e6057c2df56e6893", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006406"}, "id": "code_006406_unit_vector_006406", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006406(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": "validation", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006406"}, "verifier": {"function": "unit_vector_006406", "tests": ["ux, uy = unit_vector_006406(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006406(0, 5) == (0, 1)", "try:\n    unit_vector_006406(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_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\": [-429.3664, 191.1662], \"unit\": \"N\"}", "dedupe_signature": "dff5c8327db7ed6658950f4c045198b6c31f9824675c43113945ccb4ac180a10", "difficulty": "medium", "final_answer": {"answer": [-429.3664, 191.1662], "unit": "N"}, "id": "vector_components_006421_470_156", "license": "Apache-2.0", "prompt": "A vector has magnitude 470 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 156, "magnitude": 470.0}, "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. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 165.5 / 100.\nFinal: {\"answer\": 1.655, \"unit\": \"m\"}", "dedupe_signature": "ce1299a3ac61bd5d4e042161ff79591907846e6ebff32172135d38963bd2f162", "difficulty": "easy", "final_answer": {"answer": 1.655, "unit": "m"}, "id": "unit_convert_006438_cm_to_m_165.5", "license": "Apache-2.0", "prompt": "Convert 165.5 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 165.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 165.5}, "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\": [6.8, -29.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "5530e2eaef094ad11a60b8b18930384a3356995df0ce410bd61190da4b82c559", "difficulty": "medium", "final_answer": {"answer": [6.8, -29.75], "unit": "dimensionless"}, "id": "line_two_point_006512_-7.25_-4.75_6.8_-29.75", "license": "Apache-2.0", "prompt": "A line passes through points (-7.25, -79.05) and (-4.75, -62.05). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -7.25, "x2": -4.75, "y1": -79.05, "y2": -62.05}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=182.5 mg, t=127 h, and T_half=57.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 39.4802, \"unit\": \"mg\"}", "dedupe_signature": "95f3c6e1c79bd9eaa06c37d309f34abcba369a3cabadfffdf5a73ad0bbe40986", "difficulty": "medium", "final_answer": {"answer": 39.4802, "unit": "mg"}, "id": "half_life_006522_182.5_57.5_127", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 182.5 mg. Its half-life is 57.5 hours. How many mg remain after 127 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=182.5 mg, t=127 h, and T_half=57.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 127.0, "half_life": 57.5, "initial_amount": 182.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "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": "2cf65bd22028abe567ac2b2c6e807ea4f1f30e06285aae65cf6f5095d2b73ea3", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006549_consistent_5ca82cb9_53959", "license": "Apache-2.0", "prompt": "In sensor calibration case 53959, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.95 kg and a = 11.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 260.4825, \"unit\": \"N\"}", "dedupe_signature": "ed65147444d89bdbed897bfb53edd1bae8aa32a15a873da3bc6803b12b3b3a45", "difficulty": "easy", "final_answer": {"answer": 260.4825, "unit": "N"}, "id": "force_006552_22.95_11.35", "license": "Apache-2.0", "prompt": "A cart has mass 22.95 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 = 22.95 kg and a = 11.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.35, "mass": 22.95}, "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=84 degrees through the sine of 2 theta.\n3. Substitute v=63.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 85.7283, \"unit\": \"m\"}", "dedupe_signature": "62518872a6c8e75f674d5c773873e81d684ee1fa673d3d2d0d37cbb679f089b4", "difficulty": "medium", "final_answer": {"answer": 85.7283, "unit": "m"}, "id": "projectile_range_006554_63.6_84", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 63.6 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=63.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 84, "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. 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=71.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 374.867, \"unit\": \"m\"}", "dedupe_signature": "7a236ebd1e6b26d320dd3154e0c5f551584be0b4ef5f19b687b33f859f3fa9b8", "difficulty": "medium", "final_answer": {"answer": 374.867, "unit": "m"}, "id": "projectile_range_006572_71.5_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71.5 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=71.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 71.5}, "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=103.1 V and R=177.2 ohm.\nFinal: {\"answer\": 59.9865, \"unit\": \"W\"}", "dedupe_signature": "5c24277e4a4962977b85f1edc2b3dd117b9c233bb3dd2f076514caa357f6b81f", "difficulty": "easy", "final_answer": {"answer": 59.9865, "unit": "W"}, "id": "ohm_power_006575_103.1_177.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 177.2 ohm and voltage 103.1 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=103.1 V and R=177.2 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 177.2, "voltage": 103.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.28 * 8.314 * 583 / 41.7.\nFinal: {\"answer\": 381.2557, \"unit\": \"kPa\"}", "dedupe_signature": "c7486ce814b1306d545d67dead537e6ae2c2cd99c6380104cf398d0b72446967", "difficulty": "medium", "final_answer": {"answer": 381.2557, "unit": "kPa"}, "id": "ideal_gas_006591_3.28_583_41.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.28 mol, T=583 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 = 3.28 * 8.314 * 583 / 41.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 3.28, "temp_k": 583, "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1770 mL to 1.77 L.\n3. Compute M = 4.56 / 1.77.\nFinal: {\"answer\": 2.5763, \"unit\": \"mol/L\"}", "dedupe_signature": "977edf6ab6d40e92aee7302c89d7d3faf17d50fae8afedb712a9522310410063", "difficulty": "medium", "final_answer": {"answer": 2.5763, "unit": "mol/L"}, "id": "molarity_006596_4.56_1770", "license": "Apache-2.0", "prompt": "A solution contains 4.56 mol of solute in 1770 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1770 mL to 1.77 L.\nCompute M = 4.56 / 1.77.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.56, "volume_ml": 1770}, "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(-0.2)=11.3 and f(5.1)=-4.6.\n3. The interval width is 5.3.\nFinal: {\"answer\": 17.755, \"unit\": \"area_units\"}", "dedupe_signature": "6fbd6cadae7607571935f9a842004d777047898cfc2cd6583562f79b60a4b183", "difficulty": "medium", "final_answer": {"answer": 17.755, "unit": "area_units"}, "id": "trapz_linear_006616_-3_10.7_-0.2_5.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3x+10.7 from x=-0.2 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(-0.2)=11.3 and f(5.1)=-4.6.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 10.7, "slope": -3.0, "x0": -0.2, "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=160.3 V and R=121.5 ohm.\nFinal: {\"answer\": 211.4905, \"unit\": \"W\"}", "dedupe_signature": "cf6fd8e7f05e3b3a5a430160217e475eb5e0d764cf7fbed289850303abf0e300", "difficulty": "easy", "final_answer": {"answer": 211.4905, "unit": "W"}, "id": "ohm_power_006629_160.3_121.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 121.5 ohm and voltage 160.3 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=160.3 V and R=121.5 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 121.5, "voltage": 160.3}, "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) = -0.92 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\": 12.155, \"unit\": \"state_units\"}", "dedupe_signature": "3847b04aea2f347fe5dc9879bb946235b09188f78466c575c4a0521327dc0c70", "difficulty": "medium", "final_answer": {"answer": 12.155, "unit": "state_units"}, "id": "euler_decay_006633_39_0.92_0.35_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.92 y with y(0)=39, 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) = -0.92 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 39.0, "rate": 0.92, "step": 0.35, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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=65.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 397.8891, \"unit\": \"m\"}", "dedupe_signature": "399ba08680aa3ee77bbeb9164e98aaafff72f31c878929c4dc72aaccd820549e", "difficulty": "medium", "final_answer": {"answer": 397.8891, "unit": "m"}, "id": "projectile_range_006662_65.9_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 65.9 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=65.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4985 mL to 4.985 L.\n3. Compute M = 0.555 / 4.985.\nFinal: {\"answer\": 0.1113, \"unit\": \"mol/L\"}", "dedupe_signature": "1683ac5cd4266178ae665caa8f337aff345e3983c1d95b95c0e3a4021c57f126", "difficulty": "medium", "final_answer": {"answer": 0.1113, "unit": "mol/L"}, "id": "molarity_006668_0.555_4985", "license": "Apache-2.0", "prompt": "A solution contains 0.555 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 = 0.555 / 4.985.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 0.555, "volume_ml": 4985}, "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=0.1 and add it to the current value.\nFinal: {\"answer\": [1.175, -0.575, 0.525], \"unit\": \"temperature_units\"}", "dedupe_signature": "ba97336b624df2400137e31dc8f7a2911ac46c72388112fcab985841ac2c2c7c", "difficulty": "hard", "final_answer": {"answer": [1.175, -0.575, 0.525], "unit": "temperature_units"}, "id": "heat_step_006671_0.1_1.55_1.4_-1.0_0.85_-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=1.55, right=-0.55; current interior values are [1.4, -1.0, 0.85]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, -1.0, 0.85], "left": 1.55, "r": 0.1, "right": -0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R 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 * 615 / 75.2.\nFinal: {\"answer\": 89.0715, \"unit\": \"kPa\"}", "dedupe_signature": "741a9105b1b868f2c11a2c6129d4226178e9b0b59e33e927e0bbe0dd090003e4", "difficulty": "medium", "final_answer": {"answer": 89.0715, "unit": "kPa"}, "id": "ideal_gas_006681_1.31_615_75.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.31 mol, T=615 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 = 1.31 * 8.314 * 615 / 75.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 1.31, "temp_k": 615, "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. 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, 4.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3757d258581eea837c243b61bbc2d110422f99a002848935198ddef9371e2aff", "difficulty": "medium", "final_answer": {"answer": [4.3, 4.75], "unit": "dimensionless"}, "id": "line_two_point_006692_-10.5_-1.5_4.3_4.75", "license": "Apache-2.0", "prompt": "A line passes through points (-10.5, -40.4) and (-1.5, -1.7). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -10.5, "x2": -1.5, "y1": -40.4, "y2": -1.6999999999999993}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-1.108, -0.686, 0.372], \"unit\": \"temperature_units\"}", "dedupe_signature": "f8120189bc039486f1992977eb29f7179312eadaba95be750ae5327b2c3b4bde", "difficulty": "hard", "final_answer": {"answer": [-1.108, -0.686, 0.372], "unit": "temperature_units"}, "id": "heat_step_006707_0.24_0.4_-1.6_-1.55_2.1_-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=0.4, right=-1.45; current interior values are [-1.6, -1.55, 2.1]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-1.6, -1.55, 2.1], "left": 0.4, "r": 0.24, "right": -1.45}, "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\": [2.9, 25.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "a3ab2e555c15a1876ec77f3a841b996170025262ea28a4d184a5133e31a98de1", "difficulty": "medium", "final_answer": {"answer": [2.9, 25.5], "unit": "dimensionless"}, "id": "line_two_point_006728_-10.75_-5_2.9_25.5", "license": "Apache-2.0", "prompt": "A line passes through points (-10.75, -5.675) and (-5, 11). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "linear_modeling", "variables": {"x1": -10.75, "x2": -5.0, "y1": -5.675000000000001, "y2": 11.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=705.5 mg, t=13.5 h, and T_half=111 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 648.4631, \"unit\": \"mg\"}", "dedupe_signature": "b3fc8744baa672741711b854394e4c1b8136b079dbacca6ad0289e325b1c87f3", "difficulty": "medium", "final_answer": {"answer": 648.4631, "unit": "mg"}, "id": "half_life_006738_705.5_111_13.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 705.5 mg. Its half-life is 111 hours. How many mg remain after 13.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=705.5 mg, t=13.5 h, and T_half=111 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 13.5, "half_life": 111.0, "initial_amount": 705.5}, "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(-7.1)=-3.57 and f(-0.8)=-11.76.\n3. The interval width is 6.3.\nFinal: {\"answer\": -48.2895, \"unit\": \"area_units\"}", "dedupe_signature": "f183f64d1ee585adf5caf23bbe6f2641bee20c17846dc793d666edf00ff1314c", "difficulty": "medium", "final_answer": {"answer": -48.2895, "unit": "area_units"}, "id": "trapz_linear_006742_-1.3_-12.8_-7.1_-0.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.3x+-12.8 from x=-7.1 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(-7.1)=-3.57 and f(-0.8)=-11.76.\nThe interval width is 6.3.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -12.8, "slope": -1.3, "x0": -7.1, "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. 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, -0.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "096df3c6cf316455cb5316d1681719f8d336f9987ffbe89eb04ebc01c37781e8", "difficulty": "medium", "final_answer": {"answer": [-4.8, -0.25], "unit": "dimensionless"}, "id": "line_two_point_006746_-4.25_9.75_-4.8_-0.25", "license": "Apache-2.0", "prompt": "A line passes through points (-4.25, 20.15) and (9.75, -47.05). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -4.25, "x2": 9.75, "y1": 20.15, "y2": -47.05}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.25^2 and multiply by 0.5 * 26.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13650.8203, \"unit\": \"J\"}", "dedupe_signature": "333a943fa0b9cde9a9c7e025126aec5c239946de74f055fec256d24a45c914d9", "difficulty": "easy", "final_answer": {"answer": 13650.8203, "unit": "J"}, "id": "ke_006751_26.25_32.25", "license": "Apache-2.0", "prompt": "A body of mass 26.25 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 * 26.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.25, "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 = 0.83 * 8.314 * 570 / 87.2.\nFinal: {\"answer\": 45.1073, \"unit\": \"kPa\"}", "dedupe_signature": "8c74aa7a08becf5d598074a95a221ba4e2b902b322de15af9172a5a190900018", "difficulty": "medium", "final_answer": {"answer": 45.1073, "unit": "kPa"}, "id": "ideal_gas_006753_0.83_570_87.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.83 mol, T=570 K, and V=87.2 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 = 0.83 * 8.314 * 570 / 87.2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 0.83, "temp_k": 570, "volume_l": 87.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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(-5.7)=30.77 and f(4.1)=-38.81.\n3. The interval width is 9.8.\nFinal: {\"answer\": -39.396, \"unit\": \"area_units\"}", "dedupe_signature": "84a8fc1fdd2db3c6643d3d31c579cadd139c83a892f32c29ad74fd77411f4965", "difficulty": "medium", "final_answer": {"answer": -39.396, "unit": "area_units"}, "id": "trapz_linear_006760_-7.1_-9.7_-5.7_4.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+-9.7 from x=-5.7 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(-5.7)=30.77 and f(4.1)=-38.81.\nThe interval width is 9.8.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -9.7, "slope": -7.1, "x0": -5.7, "x1": 4.1000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.95^2 and multiply by 0.5 * 24.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 21337.6053, \"unit\": \"J\"}", "dedupe_signature": "beb600f9b13e2e3ab16c9d8896568629562bc52d47c1f42bb549ec0d37a7c6ee", "difficulty": "easy", "final_answer": {"answer": 21337.6053, "unit": "J"}, "id": "ke_006769_24.25_41.95", "license": "Apache-2.0", "prompt": "A body of mass 24.25 kg moves at 41.95 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 = 41.95^2 and multiply by 0.5 * 24.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.25, "velocity": 41.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "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 * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1307.9326, \"unit\": \"g\"}", "dedupe_signature": "79456a0e6eb6524b3ce4fba4c0f8dd6591b99e8f1d355c0bc72eebbff92bee6c", "difficulty": "medium", "final_answer": {"answer": 1307.9326, "unit": "g"}, "id": "stoich_mass_006775_glucose_7.26", "license": "Apache-2.0", "prompt": "A sample contains 7.26 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 = 7.26 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.26}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 1.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "df73dc832b9a124bfca9c16b90f29b0b7ca5e7d1892d0c4e2d3aa5c17261fee2", "difficulty": "medium", "final_answer": {"answer": [-9.75, 1.0], "unit": "dimensionless"}, "id": "line_two_point_006818_-3.25_0.25_-9.75_1", "license": "Apache-2.0", "prompt": "A line passes through points (-3.25, 32.6875) and (0.25, -1.4375). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -3.25, "x2": 0.25, "y1": 32.6875, "y2": -1.4375}, "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 normalize_006820(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_006820\"}", "dedupe_signature": "3153d3e63a28dd947ff1316040aacf55feb163da0beb77c43edf8556ad90827e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_006820"}, "id": "code_006820_normalize_006820", "license": "Apache-2.0", "prompt": "Write a Python function normalize_006820(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": "validation", "task_family": "python_code_generation", "variables": {"function": "normalize_006820"}, "verifier": {"function": "normalize_006820", "tests": ["out = normalize_006820([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_006820([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_006820([1, 1]) == [0.5, 0.5]", "try:\n    normalize_006820([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=428 mg, t=307.5 h, and T_half=84 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 33.8422, \"unit\": \"mg\"}", "dedupe_signature": "ddeecc9f3a6e1e278abd57a85bd902ed344d015c9a6071005a194ff96f159568", "difficulty": "medium", "final_answer": {"answer": 33.8422, "unit": "mg"}, "id": "half_life_006828_428_84_307.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 428 mg. Its half-life is 84 hours. How many mg remain after 307.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=428 mg, t=307.5 h, and T_half=84 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 307.5, "half_life": 84.0, "initial_amount": 428.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 9.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "66fdc13098cde15a258c5fe4b9b765a047e04abcd1641a07aebdeaf63adc8ceb", "difficulty": "medium", "final_answer": {"answer": [8.45, 9.0], "unit": "dimensionless"}, "id": "line_two_point_006836_-13.75_-8.75_8.45_9", "license": "Apache-2.0", "prompt": "A line passes through points (-13.75, -107.187) and (-8.75, -64.9375). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -13.75, "x2": -8.75, "y1": -107.18749999999999, "y2": -64.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.938, 0.109, -0.914], \"unit\": \"temperature_units\"}", "dedupe_signature": "659ff54b6099cc55b7c8cacebc50f9e4039063c15f963f974f1d4ee4edd57aa9", "difficulty": "hard", "final_answer": {"answer": [0.938, 0.109, -0.914], "unit": "temperature_units"}, "id": "heat_step_006851_0.22_-0.6_1.95_-0.1_-1.2_-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 [1.95, -0.1, -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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.95, -0.1, -1.2], "left": -0.6, "r": 0.22, "right": -1.0}, "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 pairwise_ratios_006856(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_006856\"}", "dedupe_signature": "faf45879a1888eb31bf490e02ee2f401595ab1f367526f9a342b5b4ce397eae0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_006856"}, "id": "code_006856_pairwise_ratios_006856", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_006856(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": "validation", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_006856"}, "verifier": {"function": "pairwise_ratios_006856", "tests": ["assert pairwise_ratios_006856([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_006856([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_006856([1, 2], [1])\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=40 degrees through the sine of 2 theta.\n3. Substitute v=17.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 32.1654, \"unit\": \"m\"}", "dedupe_signature": "4ef05ec01b2fe71deeafd4e69997634d4747790b568ef021d1bdf70409743bcc", "difficulty": "medium", "final_answer": {"answer": 32.1654, "unit": "m"}, "id": "projectile_range_006860_17.9_40", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 17.9 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=17.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 40, "gravity": 9.81, "speed": 17.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.65 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 165.1436, \"unit\": \"g\"}", "dedupe_signature": "f133375f20e855ca1e1c2c845ce6c18f31b52c3836f6c2693c8bac4485140cf3", "difficulty": "medium", "final_answer": {"answer": 165.1436, "unit": "g"}, "id": "stoich_mass_006865_calcium_carbonate_1.65", "license": "Apache-2.0", "prompt": "A sample contains 1.65 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 = 1.65 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.65}, "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(-9.6)=-68.22 and f(-5.6)=-39.42.\n3. The interval width is 4.\nFinal: {\"answer\": -215.28, \"unit\": \"area_units\"}", "dedupe_signature": "2c8c0f714153b46cfad5c0d794d7292b960f19d32c8d538faf89f0fcd0173a78", "difficulty": "medium", "final_answer": {"answer": -215.28, "unit": "area_units"}, "id": "trapz_linear_006886_7.2_0.9_-9.6_-5.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.2x+0.9 from x=-9.6 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(-9.6)=-68.22 and f(-5.6)=-39.42.\nThe interval width is 4.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 0.9, "slope": 7.2, "x0": -9.6, "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. 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 2 steps and round the final state.\nFinal: {\"answer\": 42.6375, \"unit\": \"state_units\"}", "dedupe_signature": "c6816588575fcc6c204ced995c8cb39fd1ebc7348168b825b70a97a9c5b99a82", "difficulty": "medium", "final_answer": {"answer": 42.6375, "unit": "state_units"}, "id": "euler_decay_006903_54.5_0.21_0.55_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=54.5, step size h=0.55, 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) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 54.5, "rate": 0.21, "step": 0.55, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_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\": [-199.2433, -173.1996], \"unit\": \"N\"}", "dedupe_signature": "d7fb2db66fae3f4bbbe45af83b4c4e23a3f057cb34fac3b895b6af054c49c79a", "difficulty": "medium", "final_answer": {"answer": [-199.2433, -173.1996], "unit": "N"}, "id": "vector_components_006907_264_221", "license": "Apache-2.0", "prompt": "A vector has magnitude 264 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 221, "magnitude": 264.0}, "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, 26.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "b6169750660383f3b14497a69fa5ddcc631c12fe7bd4cda89f8451c6d11c2f7f", "difficulty": "medium", "final_answer": {"answer": [8.2, 26.25], "unit": "dimensionless"}, "id": "line_two_point_006962_-9.5_-8.25_8.2_26.25", "license": "Apache-2.0", "prompt": "A line passes through points (-9.5, -51.65) and (-8.25, -41.4). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -9.5, "x2": -8.25, "y1": -51.64999999999999, "y2": -41.39999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=723 mg, t=104 h, and T_half=5.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0015, \"unit\": \"mg\"}", "dedupe_signature": "fcbde5d23fddb75029bb58d4847c8e2f6d8bd5f2d2ebfa021464e314cd337247", "difficulty": "medium", "final_answer": {"answer": 0.0015, "unit": "mg"}, "id": "half_life_006972_723_5.5_104", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 723 mg. Its half-life is 5.5 hours. How many mg remain after 104 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=723 mg, t=104 h, and T_half=5.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 104.0, "half_life": 5.5, "initial_amount": 723.0}, "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) = -0.96 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\": 21.7051, \"unit\": \"state_units\"}", "dedupe_signature": "9c5aa50c01ed4adc9c209a608dda3246c6dbe7a461234a25e09fba9dd1c927ae", "difficulty": "medium", "final_answer": {"answer": 21.7051, "unit": "state_units"}, "id": "euler_decay_006975_78_0.96_0.2_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.96 y with y(0)=78, 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) = -0.96 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 78.0, "rate": 0.96, "step": 0.2, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_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 * 2.26 * 66.\nFinal: {\"answer\": 55189.2, \"unit\": \"J\"}", "dedupe_signature": "77806830769d4029e8383aa6baa25a0b2729ba5cf80ffaad814e8847109cc284", "difficulty": "easy", "final_answer": {"answer": 55189.2, "unit": "J"}, "id": "heat_q_006988_370_2.26_66", "license": "Apache-2.0", "prompt": "A 370 g sample has specific heat 2.26 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 = 370 * 2.26 * 66.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 66, "heat_capacity": 2.26, "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=41.2 V and R=10.5 ohm.\nFinal: {\"answer\": 161.661, \"unit\": \"W\"}", "dedupe_signature": "6e93b68444fe8c98ad351639280d83eed79e5f5a7e7ca5a10c7ca36923500c1a", "difficulty": "easy", "final_answer": {"answer": 161.661, "unit": "W"}, "id": "ohm_power_006989_41.2_10.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 10.5 ohm and voltage 41.2 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=41.2 V and R=10.5 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 10.5, "voltage": 41.2}, "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) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 2.5792, \"unit\": \"state_units\"}", "dedupe_signature": "4bc4392beca5deaa5f52632d733eb5c08dbd93b87fe9b002b087d65faded5746", "difficulty": "medium", "final_answer": {"answer": 2.5792, "unit": "state_units"}, "id": "euler_decay_006993_3_0.03_0.5_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=3, 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) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 3.0, "rate": 0.03, "step": 0.5, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -1.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "b01c60c8cfa147baafb5293c847c7075312b09adad97e00f3a4e493770e6de75", "difficulty": "medium", "final_answer": {"answer": [5.1, -1.75], "unit": "dimensionless"}, "id": "line_two_point_006998_0.75_2.75_5.1_-1.75", "license": "Apache-2.0", "prompt": "A line passes through points (0.75, 2.075) and (2.75, 12.275). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 0.75, "x2": 2.75, "y1": 2.0749999999999997, "y2": 12.274999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - 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": "6269006f680921088657d923e2848a72a089abb8c5ab74f0c09cec0b27dfe2f5", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006999_inconsistent_7481c798_862040", "license": "Apache-2.0", "prompt": "In quality-control check case 862040, 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": "validation", "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=48 degrees through the sine of 2 theta.\n3. Substitute v=18.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 36.2134, \"unit\": \"m\"}", "dedupe_signature": "f3eb3be146d33d2506fd9ddb331fd702129a8a6be0f34d3b56e50317e04cca2c", "difficulty": "medium", "final_answer": {"answer": 36.2134, "unit": "m"}, "id": "projectile_range_007004_18.9_48", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 18.9 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=18.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 48, "gravity": 9.81, "speed": 18.9}, "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 = 90 * 2.735 * 33.\nFinal: {\"answer\": 8122.95, \"unit\": \"J\"}", "dedupe_signature": "4820ffa46186eae682212869f902b411518866496333b888bab9dcaa355a19d6", "difficulty": "easy", "final_answer": {"answer": 8122.95, "unit": "J"}, "id": "heat_q_007024_90_2.735_33", "license": "Apache-2.0", "prompt": "A 90 g sample has specific heat 2.735 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 = 90 * 2.735 * 33.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 33, "heat_capacity": 2.735, "mass_g": 90}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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)=6.49 and f(3.2)=15.46.\n3. The interval width is 3.9.\nFinal: {\"answer\": 42.8025, \"unit\": \"area_units\"}", "dedupe_signature": "050a16f0ad576a889bf8c5ebf9d7991570b1f61674455a2e9ddc66c5e9224686", "difficulty": "medium", "final_answer": {"answer": 42.8025, "unit": "area_units"}, "id": "trapz_linear_007030_2.3_8.1_-0.7_3.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.3x+8.1 from x=-0.7 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(-0.7)=6.49 and f(3.2)=15.46.\nThe interval width is 3.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 8.1, "slope": 2.3, "x0": -0.7, "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=128.4 V and R=7.2 ohm.\nFinal: {\"answer\": 2289.8, \"unit\": \"W\"}", "dedupe_signature": "3770ed8ea6e49ff2a5643b5a7baa2eda26e7ee9c4df33ca5f1d7e6952dea27c3", "difficulty": "easy", "final_answer": {"answer": 2289.8, "unit": "W"}, "id": "ohm_power_007043_128.4_7.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 7.2 ohm and voltage 128.4 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=128.4 V and R=7.2 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 7.2, "voltage": 128.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.25 kg and a = 1.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 1.9375, \"unit\": \"N\"}", "dedupe_signature": "358173e40f35b96956c3cfefbe55aa04289252937cc0bcaa6903af0ff7cfb39a", "difficulty": "easy", "final_answer": {"answer": 1.9375, "unit": "N"}, "id": "force_007056_1.25_1.55", "license": "Apache-2.0", "prompt": "A cart has mass 1.25 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 = 1.25 kg and a = 1.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.55, "mass": 1.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=99 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-25.4206, 160.4994], \"unit\": \"N\"}", "dedupe_signature": "9916ccd38ff983188040ba0b775d921ae9c7d5ea8c8af229276f812f2044e21f", "difficulty": "medium", "final_answer": {"answer": [-25.4206, 160.4994], "unit": "N"}, "id": "vector_components_007069_162.5_99", "license": "Apache-2.0", "prompt": "A vector has magnitude 162.5 N at 99 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=99 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 99, "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. 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": "75b0b59c921f9c1bbd863c48be71164e146786651eeb11531ae6656cc6c51b19", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007071_inconsistent_7481c798_793704", "license": "Apache-2.0", "prompt": "In lab notebook case 793704, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"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": "827726cecd4414fec89e9aec2328a01ca6c4fb80b9378faf23652c829c900e0d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007089_consistent_4153435f_758633", "license": "Apache-2.0", "prompt": "In instrument manual case 758633, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"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 3 steps and round the final state.\nFinal: {\"answer\": -0.0893, \"unit\": \"state_units\"}", "dedupe_signature": "6791ab61914b71b54593342373128737c8f136fe2ab93bd7c31dabb772a4ef45", "difficulty": "medium", "final_answer": {"answer": -0.0893, "unit": "state_units"}, "id": "euler_decay_007101_75_0.79_1.4_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.79 y with y(0)=75, step size h=1.4, 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) = -0.79 y, so each step multiplies y by 1 - h*0.79.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 75.0, "rate": 0.79, "step": 1.4, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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=20.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 18.1108, \"unit\": \"m\"}", "dedupe_signature": "ca753404dc16f8412aa708f03ebb5cf74a40cff050006e5dc996d4f626e9bf93", "difficulty": "medium", "final_answer": {"answer": 18.1108, "unit": "m"}, "id": "projectile_range_007112_20.9_78", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20.9 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=20.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 78, "gravity": 9.81, "speed": 20.9}, "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 = 875 * 2.97 * 105.\nFinal: {\"answer\": 272868.75, \"unit\": \"J\"}", "dedupe_signature": "6ebe0625993c1784ea928a87b5501e7c3b9277c7fa3a7a5c0836d344e803732a", "difficulty": "easy", "final_answer": {"answer": 272868.75, "unit": "J"}, "id": "heat_q_007114_875_2.97_105", "license": "Apache-2.0", "prompt": "A 875 g sample has specific heat 2.97 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 = 875 * 2.97 * 105.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 105, "heat_capacity": 2.97, "mass_g": 875}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=38 V and R=6.9 ohm.\nFinal: {\"answer\": 209.2754, \"unit\": \"W\"}", "dedupe_signature": "44c9a3a4fc1b4a24bb6303f1bf4d1a3c9f37255785454fbacb1ca920abadbdda", "difficulty": "easy", "final_answer": {"answer": 209.2754, "unit": "W"}, "id": "ohm_power_007115_38_6.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 6.9 ohm and voltage 38 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=38 V and R=6.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 6.9, "voltage": 38.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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 * 3.395 * 33.\nFinal: {\"answer\": 69461.7, \"unit\": \"J\"}", "dedupe_signature": "e3ba643ed4b0d7ebb984b89331553976b7a65428b055c8c99d6ce574df0a71a1", "difficulty": "easy", "final_answer": {"answer": 69461.7, "unit": "J"}, "id": "heat_q_007132_620_3.395_33", "license": "Apache-2.0", "prompt": "A 620 g sample has specific heat 3.395 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 = 620 * 3.395 * 33.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 33, "heat_capacity": 3.395, "mass_g": 620}, "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 = 0.63 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 11.3495, \"unit\": \"g\"}", "dedupe_signature": "ffa6f2a86eede08cea47465068d76922cb40ff26e69e818df00eb50dfc26bb75", "difficulty": "medium", "final_answer": {"answer": 11.3495, "unit": "g"}, "id": "stoich_mass_007135_water_0.63", "license": "Apache-2.0", "prompt": "A sample contains 0.63 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 = 0.63 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.63}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "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=84.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 658.8444, \"unit\": \"m\"}", "dedupe_signature": "3f58006244e5729f81fa5d1f636771b410ce04e8ef6b4c81259ea41186a6aab6", "difficulty": "medium", "final_answer": {"answer": 658.8444, "unit": "m"}, "id": "projectile_range_007148_84.8_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 84.8 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=84.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 84.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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 7 steps and round the final state.\nFinal: {\"answer\": 34.673, \"unit\": \"state_units\"}", "dedupe_signature": "f84e5caa73c4219cb63a09e477139928918dabbebba95269c18121cdba42b950", "difficulty": "medium", "final_answer": {"answer": 34.673, "unit": "state_units"}, "id": "euler_decay_007155_58.5_0.72_0.1_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.72 y with y(0)=58.5, 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) = -0.72 y, so each step multiplies y by 1 - h*0.72.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.72, "step": 0.1, "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=0.42 and add it to the current value.\nFinal: {\"answer\": [-0.403, 1.615, 0.185], \"unit\": \"temperature_units\"}", "dedupe_signature": "0321a5a3e556363c7564e46cf5c3220fe65ffa0d1084c74c922d5b3f49866d22", "difficulty": "hard", "final_answer": {"answer": [-0.403, 1.615, 0.185], "unit": "temperature_units"}, "id": "heat_step_007157_0.42_-1.15_2.6_-0.8_1.55_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=-1.15, right=0.65; current interior values are [2.6, -0.8, 1.55]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, -0.8, 1.55], "left": -1.15, "r": 0.42, "right": 0.65}, "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": "3f1d323d5d59857ea21174db40430aa9235eab7cb16392e6df9494774cef86aa", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007161_inconsistent_7481c798_400475", "license": "Apache-2.0", "prompt": "In quality-control check case 400475, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.15, -0.25, -1.07], \"unit\": \"temperature_units\"}", "dedupe_signature": "813ac28c61def07463bfe5044434db412fa850138cb72cb24bf7156872d71f9c", "difficulty": "hard", "final_answer": {"answer": [0.15, -0.25, -1.07], "unit": "temperature_units"}, "id": "heat_step_007175_0.2_2.95_-0.85_0.35_-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=2.95, right=-1.35; current interior values are [-0.85, 0.35, -1.45]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.85, 0.35, -1.45], "left": 2.95, "r": 0.2, "right": -1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.86 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1055.7142, \"unit\": \"g\"}", "dedupe_signature": "63c709b5bde71c79cea8ad28b7757d6c0ead30938fe7f0418e6045a2b58949ba", "difficulty": "medium", "final_answer": {"answer": 1055.7142, "unit": "g"}, "id": "stoich_mass_007189_glucose_5.86", "license": "Apache-2.0", "prompt": "A sample contains 5.86 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 = 5.86 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.86}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [-192.7831, -186.1684], \"unit\": \"N\"}", "dedupe_signature": "913b15fc26829d92f171bbbd769db1e8d3430d468439b6f75e4df3a2ee33e36b", "difficulty": "medium", "final_answer": {"answer": [-192.7831, -186.1684], "unit": "N"}, "id": "vector_components_007195_268_224", "license": "Apache-2.0", "prompt": "A vector has magnitude 268 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 224, "magnitude": 268.0}, "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": "d259eb3493874ed59dc7f607f01160ce06e9dc5d9d67a5f14e2d8716bfd76c03", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007233_consistent_b7d3eed1_308431", "license": "Apache-2.0", "prompt": "In field worksheet case 308431, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_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 * 3.12 * 36.\nFinal: {\"answer\": 50544.0, \"unit\": \"J\"}", "dedupe_signature": "d86f3a667542255527e52ba19f83e8bfb9175b03790220afcd8162e2ce4bb36c", "difficulty": "easy", "final_answer": {"answer": 50544.0, "unit": "J"}, "id": "heat_q_007240_450_3.12_36", "license": "Apache-2.0", "prompt": "A 450 g sample has specific heat 3.12 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 = 450 * 3.12 * 36.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 36, "heat_capacity": 3.12, "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=135.1 V and R=68.9 ohm.\nFinal: {\"answer\": 264.9058, \"unit\": \"W\"}", "dedupe_signature": "7be70eb850e59193019e71f395b18472b78b37a268128073db4d6df203740ce8", "difficulty": "easy", "final_answer": {"answer": 264.9058, "unit": "W"}, "id": "ohm_power_007241_135.1_68.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 68.9 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=68.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 68.9, "voltage": 135.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "786d19a052d32e0959370ae041e09b1f9f8a00d989eb379263c0e097d64fe2a9", "difficulty": "medium", "final_answer": {"answer": [-8.35, 7.5], "unit": "dimensionless"}, "id": "line_two_point_007250_-17.75_-17.5_-8.35_7.5", "license": "Apache-2.0", "prompt": "A line passes through points (-17.75, 155.713) and (-17.5, 153.625). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -17.75, "x2": -17.5, "y1": 155.7125, "y2": 153.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "88d3182911e58f13ca6904dd5f91cf6b73c9bf89b0418ff0c538e8adcc1b9957", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_007253_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.9 mol and T=454 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": "validation", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"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 and f(5.7)=-20.4.\n3. The interval width is 9.7.\nFinal: {\"answer\": -103.79, \"unit\": \"area_units\"}", "dedupe_signature": "3caf553f6960d687fa436355c4cb40c96dc715b647381fd58f01219f382ef08a", "difficulty": "medium", "final_answer": {"answer": -103.79, "unit": "area_units"}, "id": "trapz_linear_007264_-2_-9_-4_5.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2x+-9 from x=-4 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(-4)=-1 and f(5.7)=-20.4.\nThe interval width is 9.7.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -9.0, "slope": -2.0, "x0": -4.0, "x1": 5.699999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 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=291.5 mg, t=204.5 h, and T_half=105.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 76.0546, \"unit\": \"mg\"}", "dedupe_signature": "75388db7f8204bce7566ef065ecee26274eff2616b976aaf7c2d0623ade78a95", "difficulty": "medium", "final_answer": {"answer": 76.0546, "unit": "mg"}, "id": "half_life_007278_291.5_105.5_204.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 291.5 mg. Its half-life is 105.5 hours. How many mg remain after 204.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=291.5 mg, t=204.5 h, and T_half=105.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 204.5, "half_life": 105.5, "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. The function contract has a 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_007288(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_007288\"}", "dedupe_signature": "e1c196228dd71e69363de83a50edf0b1c74b414460a3ea95d4a340444b05c991", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007288"}, "id": "code_007288_center_values_007288", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007288(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": "validation", "task_family": "python_code_generation", "variables": {"function": "center_values_007288"}, "verifier": {"function": "center_values_007288", "tests": ["out = center_values_007288([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007288([5]) == [0]", "try:\n    center_values_007288([])\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": "cbb7d5880b8c0f4127e73599e27412ffb7309f6528bc7c2c8a469393a911f90c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007289_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 1746 items and budget 61225, 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": "validation", "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=211.2 V and R=103.7 ohm.\nFinal: {\"answer\": 430.1392, \"unit\": \"W\"}", "dedupe_signature": "6adf9efe6e854fda45a9fbb9e0ae9156f09124a1a112fb11d69304703c3fc101", "difficulty": "easy", "final_answer": {"answer": 430.1392, "unit": "W"}, "id": "ohm_power_007295_211.2_103.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 103.7 ohm and voltage 211.2 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=211.2 V and R=103.7 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 103.7, "voltage": 211.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [-151.283, -52.0909], \"unit\": \"N\"}", "dedupe_signature": "6f2741e6f705f0980ae6cd684bb875d84d7e67217972a347dad7de5c39a18287", "difficulty": "medium", "final_answer": {"answer": [-151.283, -52.0909], "unit": "N"}, "id": "vector_components_007303_160_199", "license": "Apache-2.0", "prompt": "A vector has magnitude 160 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 199, "magnitude": 160.0}, "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\nimport math\n\ndef unit_vector_007324(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_007324\"}", "dedupe_signature": "ba487bf32ed856304392477d8adde213e348beec2ce5094ad856ccc108edf767", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_007324"}, "id": "code_007324_unit_vector_007324", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_007324(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": "validation", "task_family": "python_code_generation", "variables": {"function": "unit_vector_007324"}, "verifier": {"function": "unit_vector_007324", "tests": ["ux, uy = unit_vector_007324(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_007324(0, 5) == (0, 1)", "try:\n    unit_vector_007324(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_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\": [-489.3285, 25.6446], \"unit\": \"N\"}", "dedupe_signature": "9e59d431629d04b0c2cff40c2a8867ad91b57b4af352deba28b8e2d3399d7eef", "difficulty": "medium", "final_answer": {"answer": [-489.3285, 25.6446], "unit": "N"}, "id": "vector_components_007339_490_177", "license": "Apache-2.0", "prompt": "A vector has magnitude 490 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 177, "magnitude": 490.0}, "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\": [-8.15, -4.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "4b3a46bb599443849b5eba35aa0cc8c8a14918541237424b5d67e55c64a46c4b", "difficulty": "medium", "final_answer": {"answer": [-8.15, -4.5], "unit": "dimensionless"}, "id": "line_two_point_007340_15.25_16.25_-8.15_-4.5", "license": "Apache-2.0", "prompt": "A line passes through points (15.25, -128.788) and (16.25, -136.938). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "linear_modeling", "variables": {"x1": 15.25, "x2": 16.25, "y1": -128.78750000000002, "y2": -136.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 43.0 + 273.15.\nFinal: {\"answer\": 316.15, \"unit\": \"K\"}", "dedupe_signature": "2ffb3871d9a7a11169d182587783c8321a19c5b48c603377544a6dd3a1479863", "difficulty": "easy", "final_answer": {"answer": 316.15, "unit": "K"}, "id": "unit_convert_007356_c_to_k_43", "license": "Apache-2.0", "prompt": "Convert 43 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 43.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 43.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.5 kg and a = 12.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 289.125, \"unit\": \"N\"}", "dedupe_signature": "f6fa17ac1ffe2390196a89a9571452799de0b66c3c096c226791c8451aad0ac7", "difficulty": "easy", "final_answer": {"answer": 289.125, "unit": "N"}, "id": "force_007362_22.5_12.85", "license": "Apache-2.0", "prompt": "A cart has mass 22.5 kg and measured acceleration 12.85 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 = 22.5 kg and a = 12.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.85, "mass": 22.5}, "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=461 mg, t=15 h, and T_half=100.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 415.6914, \"unit\": \"mg\"}", "dedupe_signature": "7ad8e21e8d0b27e99663929ab2074b2e4b3531fcc7aaf6728ed97d10b7eb11e4", "difficulty": "medium", "final_answer": {"answer": 415.6914, "unit": "mg"}, "id": "half_life_007368_461_100.5_15", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 461 mg. Its half-life is 100.5 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=461 mg, t=15 h, and T_half=100.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 15.0, "half_life": 100.5, "initial_amount": 461.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R 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 * 348 / 110.9.\nFinal: {\"answer\": 118.4441, \"unit\": \"kPa\"}", "dedupe_signature": "35167ccbf7722e122d8e9993779fe9baa42c8f75e6150ef292c603b681102356", "difficulty": "medium", "final_answer": {"answer": 118.4441, "unit": "kPa"}, "id": "ideal_gas_007401_4.54_348_110.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.54 mol, T=348 K, and V=110.9 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 = 4.54 * 8.314 * 348 / 110.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.54, "temp_k": 348, "volume_l": 110.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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_007414(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_007414\"}", "dedupe_signature": "53831bb5c4b61f274ae523a1b3413783b962b134a21962049b52cc284a2d3382", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007414"}, "id": "code_007414_running_total_007414", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007414(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_007414"}, "verifier": {"function": "running_total_007414", "tests": ["assert running_total_007414([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007414(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007414([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.8 * 8.314 * 320 / 31.0.\nFinal: {\"answer\": 240.3014, \"unit\": \"kPa\"}", "dedupe_signature": "d7d8425088587a2b7dcfc11568918977e907b7c806e0eb987fe9dba887a1dcf4", "difficulty": "medium", "final_answer": {"answer": 240.3014, "unit": "kPa"}, "id": "ideal_gas_007419_2.8_320_31.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.8 mol, T=320 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 = 2.8 * 8.314 * 320 / 31.0.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 2.8, "temp_k": 320, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=333 mg, t=156 h, and T_half=77.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 82.5087, \"unit\": \"mg\"}", "dedupe_signature": "57c06925db1dd9ffa953848c24c87056b31ad781c3e0b3f9e306999c8d2b2999", "difficulty": "medium", "final_answer": {"answer": 82.5087, "unit": "mg"}, "id": "half_life_007422_333_77.5_156", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 333 mg. Its half-life is 77.5 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=333 mg, t=156 h, and T_half=77.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 156.0, "half_life": 77.5, "initial_amount": 333.0}, "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 2575 mL to 2.575 L.\n3. Compute M = 1.78 / 2.575.\nFinal: {\"answer\": 0.6913, \"unit\": \"mol/L\"}", "dedupe_signature": "fcd4f212e52a481b5bfb0a602462e1bac06de25b6f7ce723e2f3a2000c00f59a", "difficulty": "medium", "final_answer": {"answer": 0.6913, "unit": "mol/L"}, "id": "molarity_007442_1.78_2575", "license": "Apache-2.0", "prompt": "A solution contains 1.78 mol of solute in 2575 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2575 mL to 2.575 L.\nCompute M = 1.78 / 2.575.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 1.78, "volume_ml": 2575}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=79.3 V and R=7 ohm.\nFinal: {\"answer\": 898.3557, \"unit\": \"W\"}", "dedupe_signature": "09e61214dd2c9c53f8566b67e23743e6b8480b1b76707dab90dc3bbec74fa163", "difficulty": "easy", "final_answer": {"answer": 898.3557, "unit": "W"}, "id": "ohm_power_007457_79.3_7", "license": "Apache-2.0", "prompt": "A resistor has resistance 7 ohm and voltage 79.3 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=79.3 V and R=7 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 7.0, "voltage": 79.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_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\": [42.3702, -240.2931], \"unit\": \"N\"}", "dedupe_signature": "6a8919a2e3c9229b634fe3b7cbfb7b0930f7274b655c6abfd6607cc8a158fb7b", "difficulty": "medium", "final_answer": {"answer": [42.3702, -240.2931], "unit": "N"}, "id": "vector_components_007465_244_280", "license": "Apache-2.0", "prompt": "A vector has magnitude 244 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 280, "magnitude": 244.0}, "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. Use Newton's second law F = m a.\n2. Substitute m = 9.65 kg and a = 1.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 11.0975, \"unit\": \"N\"}", "dedupe_signature": "3debdf790f968ed6a5af3bdca9430f12b9b0c38bfae52676149f8c3444208f10", "difficulty": "easy", "final_answer": {"answer": 11.0975, "unit": "N"}, "id": "force_007488_9.65_1.15", "license": "Apache-2.0", "prompt": "A cart has mass 9.65 kg and measured acceleration 1.15 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 = 9.65 kg and a = 1.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.15, "mass": 9.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.109, -1.123, -0.246], \"unit\": \"temperature_units\"}", "dedupe_signature": "a0cf1cda36c531dee4904938caf91d38c406158c3d0c65829a9d3948233d3950", "difficulty": "hard", "final_answer": {"answer": [-0.109, -1.123, -0.246], "unit": "temperature_units"}, "id": "heat_step_007499_0.42_0.8_-0.55_-0.85_-1.8_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=0.8, right=0.95; current interior values are [-0.55, -0.85, -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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-0.55, -0.85, -1.8], "left": 0.8, "r": 0.42, "right": 0.95}, "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\": [-8.95, 29.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "0fb11c8e15de71eb883cf97c2042f5e13241b46baee9ee62440a480cffdc93c5", "difficulty": "medium", "final_answer": {"answer": [-8.95, 29.5], "unit": "dimensionless"}, "id": "line_two_point_007502_9.75_13.75_-8.95_29.5", "license": "Apache-2.0", "prompt": "A line passes through points (9.75, -57.7625) and (13.75, -93.5625). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 9.75, "x2": 13.75, "y1": -57.76249999999999, "y2": -93.56249999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "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=36.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 92.7939, \"unit\": \"m\"}", "dedupe_signature": "806311453498eb3ab42b9d158c809a2ff5853fc4455c79b7db33abe36e780535", "difficulty": "medium", "final_answer": {"answer": 92.7939, "unit": "m"}, "id": "projectile_range_007508_36.2_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 36.2 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=36.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=504.5 mg, t=53 h, and T_half=66 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 289.1512, \"unit\": \"mg\"}", "dedupe_signature": "483c00f95391def1ba77fcd6f8ab2dd26db7c63eb4eacfe4b4abbb3ccf759365", "difficulty": "medium", "final_answer": {"answer": 289.1512, "unit": "mg"}, "id": "half_life_007512_504.5_66_53", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 504.5 mg. Its half-life is 66 hours. How many mg remain after 53 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=504.5 mg, t=53 h, and T_half=66 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 53.0, "half_life": 66.0, "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. 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": "445a9ff224818c6f0f3ba860d115be08061ab0336533b17d09eccbe9cf439937", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_007559_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=47.5 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": "validation", "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. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.754, -0.72, 0.896], \"unit\": \"temperature_units\"}", "dedupe_signature": "22647ff8e389be6d85f33b66cb88f6e9f42d24a2d04f1598f3787f25b2e76718", "difficulty": "hard", "final_answer": {"answer": [0.754, -0.72, 0.896], "unit": "temperature_units"}, "id": "heat_step_007571_0.12_2.25_0.85_-1.35_1.7_-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=2.25, right=-1.95; current interior values are [0.85, -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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [0.85, -1.35, 1.7], "left": 2.25, "r": 0.12, "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 682.0 / 1000.\nFinal: {\"answer\": 0.682, \"unit\": \"kg\"}", "dedupe_signature": "af4929c91bbca40215f100eeaed6031b091fe481b2f87d98b0bfda3a9a154ad8", "difficulty": "easy", "final_answer": {"answer": 0.682, "unit": "kg"}, "id": "unit_convert_007590_g_to_kg_682", "license": "Apache-2.0", "prompt": "Convert 682 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 682.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 682.0}, "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. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d30d0a4b5e77fc3113f44aef5c545c2926075f8173cf895a11d97088e52c38e0", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007593_inconsistent_74ac0b02_618226", "license": "Apache-2.0", "prompt": "In simulation spec case 618226, 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": "validation", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "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=85 degrees through the sine of 2 theta.\n3. Substitute v=12.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 2.8102, \"unit\": \"m\"}", "dedupe_signature": "f182dd7604ad408aa2026ca2f073c1de9b948665e69f8f93d6a422d0f012c6de", "difficulty": "medium", "final_answer": {"answer": 2.8102, "unit": "m"}, "id": "projectile_range_007598_12.6_85", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 12.6 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=12.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 85, "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. 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=38.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 152.2978, \"unit\": \"m\"}", "dedupe_signature": "21ef49d08a8866490996d975cb1f08efa7747c3219b42315e9410f4623fe6ab6", "difficulty": "medium", "final_answer": {"answer": 152.2978, "unit": "m"}, "id": "projectile_range_007634_38.7_47", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 38.7 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=38.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 47, "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. 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\": [-221.7784, 23.3098], \"unit\": \"N\"}", "dedupe_signature": "a5f29dd6e086a379e64aee2e818f2ba1dce0c8d91625fa56622161f9559cf23e", "difficulty": "medium", "final_answer": {"answer": [-221.7784, 23.3098], "unit": "N"}, "id": "vector_components_007663_223_174", "license": "Apache-2.0", "prompt": "A vector has magnitude 223 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": "validation", "task_family": "vector_reasoning", "variables": {"angle_deg": 174, "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 function contract has a 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_007666(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_007666\"}", "dedupe_signature": "2825b8f68d53baf7d0e99fe5d68c24bb01e5b86e08b7660891a27d33943c880c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007666"}, "id": "code_007666_normalize_007666", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007666(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": "validation", "task_family": "python_code_generation", "variables": {"function": "normalize_007666"}, "verifier": {"function": "normalize_007666", "tests": ["out = normalize_007666([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007666([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007666([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007666([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": "2a1aef648414eca9f58b9513e933229029727c6e7dcaf72530e3709b6aacdde2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_007667_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry experiment record from batch 15164 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": "validation", "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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.2)=30.46 and f(7.1)=47.23.\n3. The interval width is 3.9.\nFinal: {\"answer\": 151.4955, \"unit\": \"area_units\"}", "dedupe_signature": "23a5897954b074bb3ac05973aba6d9c201e3cf7abc7a7661c2b78fdb2b90b731", "difficulty": "medium", "final_answer": {"answer": 151.4955, "unit": "area_units"}, "id": "trapz_linear_007678_4.3_16.7_3.2_7.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.3x+16.7 from x=3.2 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(3.2)=30.46 and f(7.1)=47.23.\nThe interval width is 3.9.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 16.7, "slope": 4.3, "x0": 3.2, "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=75.5 V and R=78.6 ohm.\nFinal: {\"answer\": 72.5223, \"unit\": \"W\"}", "dedupe_signature": "b9b604419741577c1b7d83752020392898c4e5de88ac495f8c7651c93dd52835", "difficulty": "easy", "final_answer": {"answer": 72.5223, "unit": "W"}, "id": "ohm_power_007691_75.5_78.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 78.6 ohm and voltage 75.5 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=75.5 V and R=78.6 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 78.6, "voltage": 75.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.45 kg and a = 1.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 20.61, \"unit\": \"N\"}", "dedupe_signature": "15fa82ea275db13786390ccfc97c580b3f11743c66e0306113643c0cc202db13", "difficulty": "easy", "final_answer": {"answer": 20.61, "unit": "N"}, "id": "force_007704_11.45_1.8", "license": "Apache-2.0", "prompt": "A cart has mass 11.45 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 = 11.45 kg and a = 1.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.8, "mass": 11.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.5 kg and a = 14.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 94.575, \"unit\": \"N\"}", "dedupe_signature": "587828d8a4d8ca422b7ffd45d3ae753aff684fe5b22f5fc098c1b8fb0a5984f4", "difficulty": "easy", "final_answer": {"answer": 94.575, "unit": "N"}, "id": "force_007722_6.5_14.55", "license": "Apache-2.0", "prompt": "A cart has mass 6.5 kg and measured acceleration 14.55 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 = 6.5 kg and a = 14.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.55, "mass": 6.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 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 = 1.185 / 2.405.\nFinal: {\"answer\": 0.4927, \"unit\": \"mol/L\"}", "dedupe_signature": "b99a9309ebda791230514d7e7eba63c4f9d953352ef14bcdb874381157abb31f", "difficulty": "medium", "final_answer": {"answer": 0.4927, "unit": "mol/L"}, "id": "molarity_007730_1.185_2405", "license": "Apache-2.0", "prompt": "A solution contains 1.185 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 = 1.185 / 2.405.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 1.185, "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) = -0.09 y, so each step multiplies y by 1 - h*0.09.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 3.2634, \"unit\": \"state_units\"}", "dedupe_signature": "8011570a7427d2da4f206ddd5a68744ac13e5e2226810f005a90a26e1c3b918c", "difficulty": "medium", "final_answer": {"answer": 3.2634, "unit": "state_units"}, "id": "euler_decay_007749_8_0.09_0.8_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=8, step size h=0.8, 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 8.0, "rate": 0.09, "step": 0.8, "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)=13.34 and f(7.8)=62.64.\n3. The interval width is 8.5.\nFinal: {\"answer\": 322.915, \"unit\": \"area_units\"}", "dedupe_signature": "9df56be2a064945bd5739ee1ca37751a64e0624a3cdecb22dc08436428ec3955", "difficulty": "medium", "final_answer": {"answer": 322.915, "unit": "area_units"}, "id": "trapz_linear_007750_5.8_17.4_-0.7_7.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.8x+17.4 from x=-0.7 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(-0.7)=13.34 and f(7.8)=62.64.\nThe interval width is 8.5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": 17.4, "slope": 5.8, "x0": -0.7, "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. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.55, -9.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "f77bc030b4d3f5c6a6c276c9a45cfaa0c69942885095fa7de23a59e39ead13a1", "difficulty": "medium", "final_answer": {"answer": [6.55, -9.0], "unit": "dimensionless"}, "id": "line_two_point_007754_-0.75_1.25_6.55_-9", "license": "Apache-2.0", "prompt": "A line passes through points (-0.75, -13.9125) and (1.25, -0.8125). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -0.75, "x2": 1.25, "y1": -13.9125, "y2": -0.8125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-1.14, 0.644, 2.06], \"unit\": \"temperature_units\"}", "dedupe_signature": "0b9958f79e42983c09883872764f7ebeada4a64b6c154d08511892760c65493b", "difficulty": "hard", "final_answer": {"answer": [-1.14, 0.644, 2.06], "unit": "temperature_units"}, "id": "heat_step_007787_0.12_-0.65_-1.5_0.65_2.75_-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=-0.65, right=-0.9; current interior values are [-1.5, 0.65, 2.75]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-1.5, 0.65, 2.75], "left": -0.65, "r": 0.12, "right": -0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.652, -1.306, 0.013], \"unit\": \"temperature_units\"}", "dedupe_signature": "f68cd54f6a03374acf3998f58bbc078384b259151c14be54a466e84ab9f23b2a", "difficulty": "hard", "final_answer": {"answer": [-0.652, -1.306, 0.013], "unit": "temperature_units"}, "id": "heat_step_007805_0.34_0.4_-1.4_-1.0_-1.5_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=0.4, right=2.45; current interior values are [-1.4, -1.0, -1.5]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, -1.0, -1.5], "left": 0.4, "r": 0.34, "right": 2.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 855 mL to 0.855 L.\n3. Compute M = 4.975 / 0.855.\nFinal: {\"answer\": 5.8187, \"unit\": \"mol/L\"}", "dedupe_signature": "760b8e3678c143466eeccf7f9d16f838630ddeaed320872fd2770740a362b610", "difficulty": "medium", "final_answer": {"answer": 5.8187, "unit": "mol/L"}, "id": "molarity_007820_4.975_855", "license": "Apache-2.0", "prompt": "A solution contains 4.975 mol of solute in 855 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 855 mL to 0.855 L.\nCompute M = 4.975 / 0.855.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "chemistry_solutions", "variables": {"moles": 4.975, "volume_ml": 855}, "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)=-11.65 and f(9.2)=-41.4.\n3. The interval width is 8.5.\nFinal: {\"answer\": -225.4625, \"unit\": \"area_units\"}", "dedupe_signature": "8cda8fd930fd2fc5723809ad6b16c5692398f0707baafa0ab46b3c1265052249", "difficulty": "medium", "final_answer": {"answer": -225.4625, "unit": "area_units"}, "id": "trapz_linear_007822_-3.5_-9.2_0.7_9.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+-9.2 from x=0.7 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(0.7)=-11.65 and f(9.2)=-41.4.\nThe interval width is 8.5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_integration", "variables": {"intercept": -9.2, "slope": -3.5, "x0": 0.7, "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. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [2.56, 1.14, -0.28], \"unit\": \"temperature_units\"}", "dedupe_signature": "93fef9c7e7711a81e44d06bb3bf32e8d18d935e0b4a8921cefc717fdc491433a", "difficulty": "hard", "final_answer": {"answer": [2.56, 1.14, -0.28], "unit": "temperature_units"}, "id": "heat_step_007823_0.2_2.8_2.8_1.6_-1.9_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=2.8, right=2.7; current interior values are [2.8, 1.6, -1.9]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [2.8, 1.6, -1.9], "left": 2.8, "r": 0.2, "right": 2.7}, "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 running_total_007828(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_007828\"}", "dedupe_signature": "0f0524de94bd529159cd41c68da415d79dde2a6301db3843d202300baf6cec76", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007828"}, "id": "code_007828_running_total_007828", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007828(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": "validation", "task_family": "python_code_generation", "variables": {"function": "running_total_007828"}, "verifier": {"function": "running_total_007828", "tests": ["assert running_total_007828([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007828(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007828([]) == []"], "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=81 degrees through the sine of 2 theta.\n3. Substitute v=43.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 59.0594, \"unit\": \"m\"}", "dedupe_signature": "b2a7a4ed18d64bf5da7d59ec3b66b752bf567bfbdd20b1189b59c4da6f859d30", "difficulty": "medium", "final_answer": {"answer": 59.0594, "unit": "m"}, "id": "projectile_range_007832_43.3_81", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 43.3 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=43.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 81, "gravity": 9.81, "speed": 43.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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 8 steps and round the final state.\nFinal: {\"answer\": 0.5525, \"unit\": \"state_units\"}", "dedupe_signature": "edf525be9e69c1d10550887bc6bcb717cfaf11a71114f4d5d7e359543dcfb416", "difficulty": "medium", "final_answer": {"answer": 0.5525, "unit": "state_units"}, "id": "euler_decay_007875_51_0.96_0.45_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.96 y with y(0)=51, step size h=0.45, 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) = -0.96 y, so each step multiplies y by 1 - h*0.96.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 51.0, "rate": 0.96, "step": 0.45, "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=0.28 and add it to the current value.\nFinal: {\"answer\": [0.444, 0.448, 1.206], \"unit\": \"temperature_units\"}", "dedupe_signature": "5373e7925fb95c67cbca0f860c1eb4e3c9799152b899b84b015b9f298854aa8a", "difficulty": "hard", "final_answer": {"answer": [0.444, 0.448, 1.206], "unit": "temperature_units"}, "id": "heat_step_007877_0.28_0.4_1.2_-0.7_1.5_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=0.4, right=2.65; current interior values are [1.2, -0.7, 1.5]. 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": "validation", "task_family": "finite_difference_pde", "variables": {"interior": [1.2, -0.7, 1.5], "left": 0.4, "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 834.0 / 100.\nFinal: {\"answer\": 8.34, \"unit\": \"m\"}", "dedupe_signature": "51d88fe1cb66069929aaf574621b44629df466d51d35a21deb444a456a944961", "difficulty": "easy", "final_answer": {"answer": 8.34, "unit": "m"}, "id": "unit_convert_007878_cm_to_m_834", "license": "Apache-2.0", "prompt": "Convert 834 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 834.0 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 834.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.47 * 8.314 * 572 / 100.5.\nFinal: {\"answer\": 211.5181, \"unit\": \"kPa\"}", "dedupe_signature": "8647aa66c6dded8c1c2156a440d87bac72fad1094c3e0a0964e1f21febe4aa09", "difficulty": "medium", "final_answer": {"answer": 211.5181, "unit": "kPa"}, "id": "ideal_gas_007905_4.47_572_100.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.47 mol, T=572 K, and V=100.5 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 = 4.47 * 8.314 * 572 / 100.5.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"n_mol": 4.47, "temp_k": 572, "volume_l": 100.5}, "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=54 mg, t=161.5 h, and T_half=32 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.6336, \"unit\": \"mg\"}", "dedupe_signature": "4773d80c8184e5e1a27e4c7ac93afa4fd6f7ae6ce894160b5e22ac76d7ad4139", "difficulty": "medium", "final_answer": {"answer": 1.6336, "unit": "mg"}, "id": "half_life_007908_54_32_161.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 54 mg. Its half-life is 32 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=54 mg, t=161.5 h, and T_half=32 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 161.5, "half_life": 32.0, "initial_amount": 54.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "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 3144.5 / 100.\nFinal: {\"answer\": 31.445, \"unit\": \"m\"}", "dedupe_signature": "dbebd10c874eae85525665b52eac7a2ed9166994bdb6fd81cebdf82faa8ca861", "difficulty": "easy", "final_answer": {"answer": 31.445, "unit": "m"}, "id": "unit_convert_007914_cm_to_m_3144.5", "license": "Apache-2.0", "prompt": "Convert 3144.5 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 3144.5 / 100.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_conversion", "variables": {"value": 3144.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.4^2 and multiply by 0.5 * 22.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1219.504, \"unit\": \"J\"}", "dedupe_signature": "09f8da1e2e41e6fe744a25b538e33d80fd2b5f8e53def5ea817fd1002ecf7573", "difficulty": "easy", "final_answer": {"answer": 1219.504, "unit": "J"}, "id": "ke_007939_22.55_10.4", "license": "Apache-2.0", "prompt": "A body of mass 22.55 kg moves at 10.4 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 = 10.4^2 and multiply by 0.5 * 22.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.55, "velocity": 10.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"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 3 steps and round the final state.\nFinal: {\"answer\": 0.9417, \"unit\": \"state_units\"}", "dedupe_signature": "b700960739ef515eda13604f66ff0c2794d4297b412b7ebf1218bb2deba30537", "difficulty": "medium", "final_answer": {"answer": 0.9417, "unit": "state_units"}, "id": "euler_decay_007947_21.5_0.37_1.75_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.37 y with y(0)=21.5, step size h=1.75, 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) = -0.37 y, so each step multiplies y by 1 - h*0.37.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 21.5, "rate": 0.37, "step": 1.75, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.0, -19.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "dc734865253458f6b85f9818716817ad953ae0b417d3f35abf577ceb44e67c24", "difficulty": "medium", "final_answer": {"answer": [3.0, -19.75], "unit": "dimensionless"}, "id": "line_two_point_007952_-14.25_-9.5_3_-19.75", "license": "Apache-2.0", "prompt": "A line passes through points (-14.25, -62.5) and (-9.5, -48.25). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": -14.25, "x2": -9.5, "y1": -62.5, "y2": -48.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=123 mg, t=16.5 h, and T_half=117 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 111.5455, \"unit\": \"mg\"}", "dedupe_signature": "3e969afa00f9bc441e278816e5cdeb1171c1d98d6220b5a326078d4ff219b12d", "difficulty": "medium", "final_answer": {"answer": 111.5455, "unit": "mg"}, "id": "half_life_007962_123_117_16.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 123 mg. Its half-life is 117 hours. How many mg remain after 16.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=123 mg, t=16.5 h, and T_half=117 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 16.5, "half_life": 117.0, "initial_amount": 123.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "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 V and R=177.9 ohm.\nFinal: {\"answer\": 10.3935, \"unit\": \"W\"}", "dedupe_signature": "81d1a4a1d5ce342f34754e588f51cf046dc30a25e386f0d21a9d617ac0cf74f4", "difficulty": "easy", "final_answer": {"answer": 10.3935, "unit": "W"}, "id": "ohm_power_007979_43_177.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 177.9 ohm and voltage 43 V across it. Compute the dissipated power 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 V and R=177.9 ohm.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "electric_circuits", "variables": {"resistance": 177.9, "voltage": 43.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -21.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "5c6ad53157f21225dc054ae5c06c6187fbd9a98d23c2681e9914dc0396b2b267", "difficulty": "medium", "final_answer": {"answer": [7.0, -21.75], "unit": "dimensionless"}, "id": "line_two_point_007988_20_33_7_-21.75", "license": "Apache-2.0", "prompt": "A line passes through points (20, 118.25) and (33, 209.25). 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": "validation", "task_family": "linear_modeling", "variables": {"x1": 20.0, "x2": 33.0, "y1": 118.25, "y2": 209.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "59ac79a2102a8be82ce1e1e26b3d40fc49708660d85a6fd74687eac6bcb84b56", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007991_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse experiment records in release 425826, 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": "validation", "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 Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 90 * 4.675 * 44.\nFinal: {\"answer\": 18513.0, \"unit\": \"J\"}", "dedupe_signature": "9ee84358a39761f921ecbbdd28b64fa2e0279c6aa1fbdbc8b85a3e111b9e844d", "difficulty": "easy", "final_answer": {"answer": 18513.0, "unit": "J"}, "id": "heat_q_007996_90_4.675_44", "license": "Apache-2.0", "prompt": "A 90 g sample has specific heat 4.675 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 = 90 * 4.675 * 44.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "thermodynamics", "variables": {"delta_t": 44, "heat_capacity": 4.675, "mass_g": 90}, "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=146 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\": 0.514, \"unit\": \"mg\"}", "dedupe_signature": "fe000b01f49e86a960a1f873dce81b773348360730c8e7dc923140cb95e1f5cc", "difficulty": "medium", "final_answer": {"answer": 0.514, "unit": "mg"}, "id": "half_life_007998_146_10_81.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 146 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=146 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": "validation", "task_family": "exponential_decay", "variables": {"elapsed_time": 81.5, "half_life": 10.0, "initial_amount": 146.0}, "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) = -0.04 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\": 14.1342, \"unit\": \"state_units\"}", "dedupe_signature": "dc21bb4d143f2deb4b2115694d04cc37d3655ebcdfc8a0e8be84a8c639c0d432", "difficulty": "medium", "final_answer": {"answer": 14.1342, "unit": "state_units"}, "id": "euler_decay_008019_17.5_0.04_1.3_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.04 y with y(0)=17.5, 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) = -0.04 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": "validation", "task_family": "numerical_ode", "variables": {"initial_y": 17.5, "rate": 0.04, "step": 1.3, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.5 kg and a = 11.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 87.75, \"unit\": \"N\"}", "dedupe_signature": "8885f223532da54f94052373ff4665eb35096812a94b8a5793708ee10e5fdc2d", "difficulty": "easy", "final_answer": {"answer": 87.75, "unit": "N"}, "id": "force_008046_7.5_11.7", "license": "Apache-2.0", "prompt": "A cart has mass 7.5 kg and measured acceleration 11.7 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 = 7.5 kg and a = 11.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "validation", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.7, "mass": 7.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}