{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=620.5 mg, t=29.5 h, and T_half=118 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 521.7762, \"unit\": \"mg\"}", "dedupe_signature": "ca81bd521dd6a24a39df8f8f7be5dac1b0210edf0845225253092c171d0c5bbc", "difficulty": "medium", "final_answer": {"answer": 521.7762, "unit": "mg"}, "id": "half_life_000006_620.5_118_29.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 620.5 mg. Its half-life is 118 hours. How many mg remain after 29.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=620.5 mg, t=29.5 h, and T_half=118 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 29.5, "half_life": 118.0, "initial_amount": 620.5}, "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\": [1.05, 16.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "5f3bd943a9fbddde55ce2f9d2d5168508f8062bc583154de372106a78b1ac083", "difficulty": "medium", "final_answer": {"answer": [1.05, 16.75], "unit": "dimensionless"}, "id": "line_two_point_000014_-9.75_-7_1.05_16.75", "license": "Apache-2.0", "prompt": "A line passes through points (-9.75, 6.5125) and (-7, 9.4). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -9.75, "x2": -7.0, "y1": 6.512499999999999, "y2": 9.399999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "91a23eacc0479507a3d38f57a76d4bd436b831d005afddf1fe812982c414effb", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000017_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 [-1.5, 2.95, -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": "test", "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. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.4, 1.329, 1.169], \"unit\": \"temperature_units\"}", "dedupe_signature": "38b939dc3ebc74d65b087eed48c2f599d37c6dbf7413d23eb20fe9323916eb8b", "difficulty": "hard", "final_answer": {"answer": [0.4, 1.329, 1.169], "unit": "temperature_units"}, "id": "heat_step_000029_0.14_2.7_-0.3_1.7_1.05_1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=1.25; current interior values are [-0.3, 1.7, 1.05]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.3, 1.7, 1.05], "left": 2.7, "r": 0.14, "right": 1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=208 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-82.1141, -43.6609], \"unit\": \"N\"}", "dedupe_signature": "f16e1f1de32f68b7e57f26024265bfe20eeee761400667566012eeb68c1fa52b", "difficulty": "medium", "final_answer": {"answer": [-82.1141, -43.6609], "unit": "N"}, "id": "vector_components_000031_93_208", "license": "Apache-2.0", "prompt": "A vector has magnitude 93 N at 208 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=208 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 208, "magnitude": 93.0}, "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 = 1.72 * 8.314 * 315 / 41.4.\nFinal: {\"answer\": 108.805, \"unit\": \"kPa\"}", "dedupe_signature": "23e911372cbd58206f1ce4e7c506e89b0f0993997c20e7d4c0719ecb619baf91", "difficulty": "medium", "final_answer": {"answer": 108.805, "unit": "kPa"}, "id": "ideal_gas_000057_1.72_315_41.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.72 mol, T=315 K, and V=41.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.72 * 8.314 * 315 / 41.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.72, "temp_k": 315, "volume_l": 41.4}, "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 325 mL to 0.325 L.\n3. Compute M = 3.185 / 0.325.\nFinal: {\"answer\": 9.8, \"unit\": \"mol/L\"}", "dedupe_signature": "6eee4a4d7739d4e5a6a72e07a32b2bf2acd3e2a0711a3b485b4df1a510737952", "difficulty": "medium", "final_answer": {"answer": 9.8, "unit": "mol/L"}, "id": "molarity_000062_3.185_325", "license": "Apache-2.0", "prompt": "A solution contains 3.185 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 = 3.185 / 0.325.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 3.185, "volume_ml": 325}, "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 = 1930 * 3.915 * 22.\nFinal: {\"answer\": 166230.9, \"unit\": \"J\"}", "dedupe_signature": "ad1744c7a2df599a2c0103c5f3eaf3e0f8a7cf3b89081e0d6368ce6674384bfa", "difficulty": "easy", "final_answer": {"answer": 166230.9, "unit": "J"}, "id": "heat_q_000076_1930_3.915_22", "license": "Apache-2.0", "prompt": "A 1930 g sample has specific heat 3.915 J/(g*K). How much heat is needed to raise its temperature by 22 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1930 * 3.915 * 22.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 22, "heat_capacity": 3.915, "mass_g": 1930}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=133.5 V and R=56.8 ohm.\nFinal: {\"answer\": 313.772, \"unit\": \"W\"}", "dedupe_signature": "45a9edfcc26ca83a27645f4b19d0ff592b7e21795abc466c39c42a9e44601b2f", "difficulty": "easy", "final_answer": {"answer": 313.772, "unit": "W"}, "id": "ohm_power_000077_133.5_56.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 56.8 ohm and voltage 133.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=133.5 V and R=56.8 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 56.8, "voltage": 133.5}, "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\": [20.8378, -118.1769], \"unit\": \"N\"}", "dedupe_signature": "9d981cdcfdd7d2f53ecef2f364f6b829aac2b143add1e349b58dd3d4e0f399ea", "difficulty": "medium", "final_answer": {"answer": [20.8378, -118.1769], "unit": "N"}, "id": "vector_components_000085_120_280", "license": "Apache-2.0", "prompt": "A vector has magnitude 120 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": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 280, "magnitude": 120.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "1e32c20a8ffaf00bc5535032d67c5f9d9d38f975c091924d2e7a1a366842dc75", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000087_inconsistent_c1271127_602167", "license": "Apache-2.0", "prompt": "In student derivation case 602167, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "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 = 790 * 1.31 * 14.\nFinal: {\"answer\": 14488.6, \"unit\": \"J\"}", "dedupe_signature": "e9e385ca2f855629203021ce26da6e909e7525b470def02e0aafb7b32c7c9f0e", "difficulty": "easy", "final_answer": {"answer": 14488.6, "unit": "J"}, "id": "heat_q_000112_790_1.31_14", "license": "Apache-2.0", "prompt": "A 790 g sample has specific heat 1.31 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 = 790 * 1.31 * 14.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 14, "heat_capacity": 1.31, "mass_g": 790}, "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 2655 mL to 2.655 L.\n3. Compute M = 0.235 / 2.655.\nFinal: {\"answer\": 0.0885, \"unit\": \"mol/L\"}", "dedupe_signature": "b887c54abcfa71b991a7e9818494631375c18b627709ff266f64aa617abafe7d", "difficulty": "medium", "final_answer": {"answer": 0.0885, "unit": "mol/L"}, "id": "molarity_000116_0.235_2655", "license": "Apache-2.0", "prompt": "A solution contains 0.235 mol of solute in 2655 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2655 mL to 2.655 L.\nCompute M = 0.235 / 2.655.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 0.235, "volume_ml": 2655}, "verifier": {"formula": "moles / (volume_ml / 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\": [-1.4, -3.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "63937600510ed3cdb14faf2beafd3f17a3bd26acafd362b701b40ab71a38e937", "difficulty": "medium", "final_answer": {"answer": [-1.4, -3.25], "unit": "dimensionless"}, "id": "line_two_point_000122_-6.5_-6.25_-1.4_-3.25", "license": "Apache-2.0", "prompt": "A line passes through points (-6.5, 5.85) and (-6.25, 5.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -6.5, "x2": -6.25, "y1": 5.85, "y2": 5.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=78.3 V and R=151.3 ohm.\nFinal: {\"answer\": 40.5214, \"unit\": \"W\"}", "dedupe_signature": "df210eb2e3df7859b1ae334e365b3b70e2fb6981677278788654c3bf06ada3fe", "difficulty": "easy", "final_answer": {"answer": 40.5214, "unit": "W"}, "id": "ohm_power_000131_78.3_151.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 151.3 ohm and voltage 78.3 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=78.3 V and R=151.3 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 151.3, "voltage": 78.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=224 mg, t=245 h, and T_half=86 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 31.093, \"unit\": \"mg\"}", "dedupe_signature": "b1f7200b5368e8a2876fbb94e2307fffad99f577a9004d46486dd8d2a84a6fff", "difficulty": "medium", "final_answer": {"answer": 31.093, "unit": "mg"}, "id": "half_life_000132_224_86_245", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 224 mg. Its half-life is 86 hours. How many mg remain after 245 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=224 mg, t=245 h, and T_half=86 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 245.0, "half_life": 86.0, "initial_amount": 224.0}, "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) = -0.62 y, so each step multiplies y by 1 - h*0.62.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 7.7254, \"unit\": \"state_units\"}", "dedupe_signature": "8d2f1dd7e9d771c79e3540b6a4e2fbbf8d35bf9f405e8c3c09d8e92cca643702", "difficulty": "medium", "final_answer": {"answer": 7.7254, "unit": "state_units"}, "id": "euler_decay_000135_53.5_0.62_1_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.62 y with y(0)=53.5, step size h=1, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 53.5, "rate": 0.62, "step": 1.0, "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) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 14.6747, \"unit\": \"state_units\"}", "dedupe_signature": "6b5d0bd026377fe5b008b0d85e83c74fe3781afd128af4f3f9f595f913ed383c", "difficulty": "medium", "final_answer": {"answer": 14.6747, "unit": "state_units"}, "id": "euler_decay_000153_38.5_0.11_1.35_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=38.5, step size h=1.35, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 38.5, "rate": 0.11, "step": 1.35, "steps": 6}, "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=42.7 V and R=153.8 ohm.\nFinal: {\"answer\": 11.8549, \"unit\": \"W\"}", "dedupe_signature": "35e17b3651ceb20bc4b584185cc66bb5cce415767744abf38aef052206c8b9c8", "difficulty": "easy", "final_answer": {"answer": 11.8549, "unit": "W"}, "id": "ohm_power_000167_42.7_153.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 153.8 ohm and voltage 42.7 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=42.7 V and R=153.8 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 153.8, "voltage": 42.7}, "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 44000.0 / 1000.\nFinal: {\"answer\": 44.0, \"unit\": \"kg\"}", "dedupe_signature": "0b0acff8e122f206df2dd5e4ac485a6cd2615317e5f8b723a33744613e2eaa18", "difficulty": "easy", "final_answer": {"answer": 44.0, "unit": "kg"}, "id": "unit_convert_000174_g_to_kg_44000", "license": "Apache-2.0", "prompt": "Convert 44000 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 44000.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 44000.0}, "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 = 935 * 0.95 * 70.\nFinal: {\"answer\": 62177.5, \"unit\": \"J\"}", "dedupe_signature": "9f2e0d9fe1065cbbfdad4ab5c380d73f033f932232f2b86b7da451df61d6ce4e", "difficulty": "easy", "final_answer": {"answer": 62177.5, "unit": "J"}, "id": "heat_q_000184_935_0.95_70", "license": "Apache-2.0", "prompt": "A 935 g sample has specific heat 0.95 J/(g*K). How much heat is needed to raise its temperature by 70 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 935 * 0.95 * 70.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 70, "heat_capacity": 0.95, "mass_g": 935}, "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 194.0 + 273.15.\nFinal: {\"answer\": 467.15, \"unit\": \"K\"}", "dedupe_signature": "43c08ea5e180f05994132a63fae2a30d4d70b3a342129ffc3c0ce3f14d2da492", "difficulty": "easy", "final_answer": {"answer": 467.15, "unit": "K"}, "id": "unit_convert_000192_c_to_k_194", "license": "Apache-2.0", "prompt": "Convert 194 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 194.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 194.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=192 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-40.5931, -8.6283], \"unit\": \"N\"}", "dedupe_signature": "22f25e1ee9037b8df1f885aa9885ad154118ecf6542ffd051fa8ba5842410900", "difficulty": "medium", "final_answer": {"answer": [-40.5931, -8.6283], "unit": "N"}, "id": "vector_components_000193_41.5_192", "license": "Apache-2.0", "prompt": "A vector has magnitude 41.5 N at 192 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=192 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 192, "magnitude": 41.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "8dcd4849fe7e7c9f3cc4c42c68740e8ddda39199c134cc4df989657bcf90cf4f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000195_consistent_5ca82cb9_992611", "license": "Apache-2.0", "prompt": "In lab notebook case 992611, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "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=0.4 and add it to the current value.\nFinal: {\"answer\": [-0.92, -0.38, 0.25], \"unit\": \"temperature_units\"}", "dedupe_signature": "0a832d5c423435a877ccafe9b89d89edccd52a2316b57d9af44c04897d81de59", "difficulty": "hard", "final_answer": {"answer": [-0.92, -0.38, 0.25], "unit": "temperature_units"}, "id": "heat_step_000209_0.4_-1.2_-1.4_-0.4_0.65_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=-1.2, right=0.7; current interior values are [-1.4, -0.4, 0.65]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, -0.4, 0.65], "left": -1.2, "r": 0.4, "right": 0.7}, "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": "7e5c090eba5722d788f1f9cccfe31fafae370533e378bcb60ec4e3b2d8072058", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_000215_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 47 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": "test", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 290 * 3.22 * 36.\nFinal: {\"answer\": 33616.8, \"unit\": \"J\"}", "dedupe_signature": "ff1070a68f6a848b514bb108c58bda2906fc206a2759f65f82f93c8862659674", "difficulty": "easy", "final_answer": {"answer": 33616.8, "unit": "J"}, "id": "heat_q_000220_290_3.22_36", "license": "Apache-2.0", "prompt": "A 290 g sample has specific heat 3.22 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 = 290 * 3.22 * 36.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 36, "heat_capacity": 3.22, "mass_g": 290}, "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=145 mg, t=12.5 h, and T_half=76 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 129.3768, \"unit\": \"mg\"}", "dedupe_signature": "1ced9debc22b3627b023fd93cb06ccc0f0eb2645971ddf3dd3f956baf066b6f6", "difficulty": "medium", "final_answer": {"answer": 129.3768, "unit": "mg"}, "id": "half_life_000222_145_76_12.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 145 mg. Its half-life is 76 hours. How many mg remain after 12.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=145 mg, t=12.5 h, and T_half=76 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 12.5, "half_life": 76.0, "initial_amount": 145.0}, "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 = 1820 * 4.295 * 100.\nFinal: {\"answer\": 781690.0, \"unit\": \"J\"}", "dedupe_signature": "79204349222a83cc83d6aafc87c3333a957b343533ba019fee66b33b436bef6a", "difficulty": "easy", "final_answer": {"answer": 781690.0, "unit": "J"}, "id": "heat_q_000238_1820_4.295_100", "license": "Apache-2.0", "prompt": "A 1820 g sample has specific heat 4.295 J/(g*K). How much heat is needed to raise its temperature by 100 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1820 * 4.295 * 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 100, "heat_capacity": 4.295, "mass_g": 1820}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=73.2 V and R=117.3 ohm.\nFinal: {\"answer\": 45.6798, \"unit\": \"W\"}", "dedupe_signature": "2826f995dbb0be80d48f1d1e0f7df3a8f062ab7e7cf9294aaf73257dc245b017", "difficulty": "easy", "final_answer": {"answer": 45.6798, "unit": "W"}, "id": "ohm_power_000239_73.2_117.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 117.3 ohm and voltage 73.2 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=73.2 V and R=117.3 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 117.3, "voltage": 73.2}, "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=20 degrees and keep the unit as newtons.\nFinal: {\"answer\": [346.2767, 126.0344], \"unit\": \"N\"}", "dedupe_signature": "0c40cbd748f649c2bceb9b7e3db73e28c8f28ce4a7719d6c026e6690c375ba35", "difficulty": "medium", "final_answer": {"answer": [346.2767, 126.0344], "unit": "N"}, "id": "vector_components_000265_368.5_20", "license": "Apache-2.0", "prompt": "A vector has magnitude 368.5 N at 20 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=20 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 20, "magnitude": 368.5}, "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_000268(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_000268\"}", "dedupe_signature": "6af67ff83220d870a2f01cc261746a49e03c2f146de2a4385940bfbdd593acae", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000268"}, "id": "code_000268_safe_mean_000268", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000268(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000268"}, "verifier": {"function": "safe_mean_000268", "tests": ["assert safe_mean_000268([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000268(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000268([])\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=184 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-253.8801, -17.753], \"unit\": \"N\"}", "dedupe_signature": "f5f285f0bb73f275c3fc1054025dcc68fe9aeb3cb751ead3f9cf3dfe5d4ab4c2", "difficulty": "medium", "final_answer": {"answer": [-253.8801, -17.753], "unit": "N"}, "id": "vector_components_000283_254.5_184", "license": "Apache-2.0", "prompt": "A vector has magnitude 254.5 N at 184 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=184 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 184, "magnitude": 254.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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=19.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 31.8679, \"unit\": \"m\"}", "dedupe_signature": "0fac2fc14465e3810dd4992c061d2c720dea5b340ab715d517d41f63d74ae031", "difficulty": "medium", "final_answer": {"answer": 31.8679, "unit": "m"}, "id": "projectile_range_000290_19.2_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 19.2 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=29 degrees through the sine of 2 theta.\nSubstitute v=19.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "gravity": 9.81, "speed": 19.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2435 mL to 2.435 L.\n3. Compute M = 2.27 / 2.435.\nFinal: {\"answer\": 0.9322, \"unit\": \"mol/L\"}", "dedupe_signature": "f139af070325c4e0a14c66be57ebaec0ff8f8a6225fa07590be6dd7858348e59", "difficulty": "medium", "final_answer": {"answer": 0.9322, "unit": "mol/L"}, "id": "molarity_000296_2.27_2435", "license": "Apache-2.0", "prompt": "A solution contains 2.27 mol of solute in 2435 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2435 mL to 2.435 L.\nCompute M = 2.27 / 2.435.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.27, "volume_ml": 2435}, "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 = 18.55 kg and a = 13 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 241.15, \"unit\": \"N\"}", "dedupe_signature": "88897400c4b56074aa85666611a5ff58d01e64fa90a5845ac1ef14bb21b0fb6b", "difficulty": "easy", "final_answer": {"answer": 241.15, "unit": "N"}, "id": "force_000324_18.55_13", "license": "Apache-2.0", "prompt": "A cart has mass 18.55 kg and measured acceleration 13 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.55 kg and a = 13 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.0, "mass": 18.55}, "verifier": {"formula": "mass * acceleration", "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 30365.0 / 1000.\nFinal: {\"answer\": 30.365, \"unit\": \"kg\"}", "dedupe_signature": "2a1670f25e95763e26730900fe06246932f958911e48c61254d36d8aba6a6ac3", "difficulty": "easy", "final_answer": {"answer": 30.365, "unit": "kg"}, "id": "unit_convert_000336_g_to_kg_30365", "license": "Apache-2.0", "prompt": "Convert 30365 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 30365.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 30365.0}, "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 = 38.9^2 and multiply by 0.5 * 6.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4993.593, \"unit\": \"J\"}", "dedupe_signature": "fc7625eb72ac7a341b48992d602c86edcb5166b74049668b1a9c033becd8027e", "difficulty": "easy", "final_answer": {"answer": 4993.593, "unit": "J"}, "id": "ke_000361_6.6_38.9", "license": "Apache-2.0", "prompt": "A body of mass 6.6 kg moves at 38.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 38.9^2 and multiply by 0.5 * 6.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.6, "velocity": 38.9}, "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 = 355 * 0.935 * 89.\nFinal: {\"answer\": 29541.325, \"unit\": \"J\"}", "dedupe_signature": "78b213945587c118edb8b682e153b2272bfa45aff36db71ed9b94078ee0773e0", "difficulty": "easy", "final_answer": {"answer": 29541.325, "unit": "J"}, "id": "heat_q_000364_355_0.935_89", "license": "Apache-2.0", "prompt": "A 355 g sample has specific heat 0.935 J/(g*K). How much heat is needed to raise its temperature by 89 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 355 * 0.935 * 89.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 89, "heat_capacity": 0.935, "mass_g": 355}, "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=108 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-9.425, 29.0072], \"unit\": \"N\"}", "dedupe_signature": "1ad8fb2a1e0b7514d5d1ec7077d879035bb8b1652f5f6a693093bf4614d94400", "difficulty": "medium", "final_answer": {"answer": [-9.425, 29.0072], "unit": "N"}, "id": "vector_components_000373_30.5_108", "license": "Apache-2.0", "prompt": "A vector has magnitude 30.5 N at 108 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=108 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 108, "magnitude": 30.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.3 * 8.314 * 344 / 65.7.\nFinal: {\"answer\": 100.1223, \"unit\": \"kPa\"}", "dedupe_signature": "de1e3e05008a1291245ff7f3d1162715d986fb2e4d221e5814a78556c06a0124", "difficulty": "medium", "final_answer": {"answer": 100.1223, "unit": "kPa"}, "id": "ideal_gas_000381_2.3_344_65.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.3 mol, T=344 K, and V=65.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.3 * 8.314 * 344 / 65.7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.3, "temp_k": 344, "volume_l": 65.7}, "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: 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": "8366e0b15eb3760031ac72d9ee5d2495017e3f6b5289926a41ad2c8b21f76ee1", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000395_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid laboratory survey records in release 391537, 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": "test", "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 the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.24 * 8.314 * 470 / 39.2.\nFinal: {\"answer\": 422.6566, \"unit\": \"kPa\"}", "dedupe_signature": "3a31bd38cf64882a09dd24c6eb83878e9f59be0895e816f4d5fe243a94c04d6e", "difficulty": "medium", "final_answer": {"answer": 422.6566, "unit": "kPa"}, "id": "ideal_gas_000399_4.24_470_39.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.24 mol, T=470 K, and V=39.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.24 * 8.314 * 470 / 39.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.24, "temp_k": 470, "volume_l": 39.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=363 mg, t=135 h, and T_half=2.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "67610360d08d11126d56c88fc02507476a279fca49d9981f2c9310b1b88eae7b", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_000402_363_2.5_135", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 363 mg. Its half-life is 2.5 hours. How many mg remain after 135 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=363 mg, t=135 h, and T_half=2.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 135.0, "half_life": 2.5, "initial_amount": 363.0}, "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 1030 mL to 1.03 L.\n3. Compute M = 4.415 / 1.03.\nFinal: {\"answer\": 4.2864, \"unit\": \"mol/L\"}", "dedupe_signature": "4a28258547502fd33ce6dd3501266c7aa566521d929567f45da3218f0bc02cd4", "difficulty": "medium", "final_answer": {"answer": 4.2864, "unit": "mol/L"}, "id": "molarity_000404_4.415_1030", "license": "Apache-2.0", "prompt": "A solution contains 4.415 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 = 4.415 / 1.03.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.415, "volume_ml": 1030}, "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 = 12.55 kg and a = 10.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 136.1675, \"unit\": \"N\"}", "dedupe_signature": "c6c4f99a37f8901c250715d7ed42f7258f881269d7056c593488ce1413075907", "difficulty": "easy", "final_answer": {"answer": 136.1675, "unit": "N"}, "id": "force_000414_12.55_10.85", "license": "Apache-2.0", "prompt": "A cart has mass 12.55 kg and measured acceleration 10.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.55 kg and a = 10.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.85, "mass": 12.55}, "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=234.5 mg, t=188.5 h, and T_half=41 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.6859, \"unit\": \"mg\"}", "dedupe_signature": "ad175d4cae87bd5f49247b0a7f0fd42649a2aa4d8bde22316dbefbb7d20caa6a", "difficulty": "medium", "final_answer": {"answer": 9.6859, "unit": "mg"}, "id": "half_life_000420_234.5_41_188.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 234.5 mg. Its half-life is 41 hours. How many mg remain after 188.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=234.5 mg, t=188.5 h, and T_half=41 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 188.5, "half_life": 41.0, "initial_amount": 234.5}, "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: 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": "eb6cd618929e643a6baa11af337e0a009ed2c5e0e6b7e3058bad61af8d9482cc", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000431_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry experiment records in release 206332, 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": "test", "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2950 mL to 2.95 L.\n3. Compute M = 4.21 / 2.95.\nFinal: {\"answer\": 1.4271, \"unit\": \"mol/L\"}", "dedupe_signature": "34e0bcff68808c91e1d5d088243d6fe36f70b0f4150bea5e9c1ec3b27b71d84c", "difficulty": "medium", "final_answer": {"answer": 1.4271, "unit": "mol/L"}, "id": "molarity_000440_4.21_2950", "license": "Apache-2.0", "prompt": "A solution contains 4.21 mol of solute in 2950 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2950 mL to 2.95 L.\nCompute M = 4.21 / 2.95.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.21, "volume_ml": 2950}, "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 3724.0 / 100.\nFinal: {\"answer\": 37.24, \"unit\": \"m\"}", "dedupe_signature": "fbb3245929cee89117c6fb1849653bbe3aea0eb74f0faeda1003e1499e611405", "difficulty": "easy", "final_answer": {"answer": 37.24, "unit": "m"}, "id": "unit_convert_000444_cm_to_m_3724", "license": "Apache-2.0", "prompt": "Convert 3724 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 3724.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 3724.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.45, 17.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3d5fb6fff6e18a3faad41febf0a49ef3f24fc7716d092752571c2d42c23753f9", "difficulty": "medium", "final_answer": {"answer": [6.45, 17.75], "unit": "dimensionless"}, "id": "line_two_point_000464_-18.5_-14.5_6.45_17.75", "license": "Apache-2.0", "prompt": "A line passes through points (-18.5, -101.575) and (-14.5, -75.775). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -18.5, "x2": -14.5, "y1": -101.575, "y2": -75.775}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_000466(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_000466\"}", "dedupe_signature": "8466b17c7199e74c942fafe0856913ad620db93dd99294a53ae1bb806d07b398", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_000466"}, "id": "code_000466_running_total_000466", "license": "Apache-2.0", "prompt": "Write a Python function running_total_000466(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": "test", "task_family": "python_code_generation", "variables": {"function": "running_total_000466"}, "verifier": {"function": "running_total_000466", "tests": ["assert running_total_000466([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_000466(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_000466([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.45 kg and a = 8.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 217.605, \"unit\": \"N\"}", "dedupe_signature": "719303255b4bc5920143eac27eb5378d55b112131759d8bc9bc97ed77ae7c89b", "difficulty": "easy", "final_answer": {"answer": 217.605, "unit": "N"}, "id": "force_000468_24.45_8.9", "license": "Apache-2.0", "prompt": "A cart has mass 24.45 kg and measured acceleration 8.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.45 kg and a = 8.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.9, "mass": 24.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1395 * 1.745 * 16.\nFinal: {\"answer\": 38948.4, \"unit\": \"J\"}", "dedupe_signature": "fe551547dfa4ee1b8033034c534d436d2fce62888c0dfac0c1c139f90e252be2", "difficulty": "easy", "final_answer": {"answer": 38948.4, "unit": "J"}, "id": "heat_q_000472_1395_1.745_16", "license": "Apache-2.0", "prompt": "A 1395 g sample has specific heat 1.745 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 = 1395 * 1.745 * 16.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 1.745, "mass_g": 1395}, "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 1280 mL to 1.28 L.\n3. Compute M = 2.365 / 1.28.\nFinal: {\"answer\": 1.8477, \"unit\": \"mol/L\"}", "dedupe_signature": "0754b2274fae4830d7658476f6797809612897155032cd1813d4c017bc176f0c", "difficulty": "medium", "final_answer": {"answer": 1.8477, "unit": "mol/L"}, "id": "molarity_000476_2.365_1280", "license": "Apache-2.0", "prompt": "A solution contains 2.365 mol of solute in 1280 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1280 mL to 1.28 L.\nCompute M = 2.365 / 1.28.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.365, "volume_ml": 1280}, "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 = 2.65 kg and a = 3.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 8.3475, \"unit\": \"N\"}", "dedupe_signature": "bab6ea43cec3eb09d221818badbb65294cb73d2e9476b866dbb947bcc7aee641", "difficulty": "easy", "final_answer": {"answer": 8.3475, "unit": "N"}, "id": "force_000504_2.65_3.15", "license": "Apache-2.0", "prompt": "A cart has mass 2.65 kg and measured acceleration 3.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.65 kg and a = 3.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.15, "mass": 2.65}, "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 * 4.245 * 67.\nFinal: {\"answer\": 480661.35, \"unit\": \"J\"}", "dedupe_signature": "683e8047ca53eaddac668bf785ff012e9acda0e7f5e532b4e1e2d3ebe0d75265", "difficulty": "easy", "final_answer": {"answer": 480661.35, "unit": "J"}, "id": "heat_q_000508_1690_4.245_67", "license": "Apache-2.0", "prompt": "A 1690 g sample has specific heat 4.245 J/(g*K). How much heat is needed to raise its temperature by 67 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1690 * 4.245 * 67.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 67, "heat_capacity": 4.245, "mass_g": 1690}, "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=339 degrees and keep the unit as newtons.\nFinal: {\"answer\": [202.587, -77.7658], \"unit\": \"N\"}", "dedupe_signature": "fe7111e7408907d7a271798330cf7a32536d44a8ddc56d2e426875917c1569ad", "difficulty": "medium", "final_answer": {"answer": [202.587, -77.7658], "unit": "N"}, "id": "vector_components_000517_217_339", "license": "Apache-2.0", "prompt": "A vector has magnitude 217 N at 339 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=339 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 339, "magnitude": 217.0}, "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. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 38.85^2 and multiply by 0.5 * 27.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 20375.8538, \"unit\": \"J\"}", "dedupe_signature": "2a901627cd933ec0e13ec9efd5868c702d8af24326dbdba8d017f50735732941", "difficulty": "easy", "final_answer": {"answer": 20375.8538, "unit": "J"}, "id": "ke_000523_27_38.85", "license": "Apache-2.0", "prompt": "A body of mass 27 kg moves at 38.85 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 = 38.85^2 and multiply by 0.5 * 27.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.0, "velocity": 38.85}, "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=317.5 mg, t=305.5 h, and T_half=84 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 25.5227, \"unit\": \"mg\"}", "dedupe_signature": "c7e76e0c30f355ea1b18fdf3cc71a91774d5ea59370dc8b092d54101516a54eb", "difficulty": "medium", "final_answer": {"answer": 25.5227, "unit": "mg"}, "id": "half_life_000528_317.5_84_305.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 317.5 mg. Its half-life is 84 hours. How many mg remain after 305.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=317.5 mg, t=305.5 h, and T_half=84 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 305.5, "half_life": 84.0, "initial_amount": 317.5}, "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=0.32 and add it to the current value.\nFinal: {\"answer\": [-1.114, -0.086, 0.524], \"unit\": \"temperature_units\"}", "dedupe_signature": "048a54e96d299069ec1e7e08b5c618971df0832cebce28e828bd50b281a4c1e8", "difficulty": "hard", "final_answer": {"answer": [-1.114, -0.086, 0.524], "unit": "temperature_units"}, "id": "heat_step_000533_0.32_-1.4_-0.65_-1.35_1.9_0.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.4, right=0.85; current interior values are [-0.65, -1.35, 1.9]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, -1.35, 1.9], "left": -1.4, "r": 0.32, "right": 0.85}, "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_000538(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_000538\"}", "dedupe_signature": "b3d7781e163afcd2f0066990cb177c394bbf3b7543ce87b69c94bfc083372cf1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_000538"}, "id": "code_000538_running_total_000538", "license": "Apache-2.0", "prompt": "Write a Python function running_total_000538(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": "test", "task_family": "python_code_generation", "variables": {"function": "running_total_000538"}, "verifier": {"function": "running_total_000538", "tests": ["assert running_total_000538([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_000538(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_000538([]) == []"], "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 = 1.12 * 8.314 * 478 / 61.2.\nFinal: {\"answer\": 72.7285, \"unit\": \"kPa\"}", "dedupe_signature": "27f189f270e0a9b22d3a5e3d1de6a591e6744b9fb2d0e044b09dd29c0c8887f2", "difficulty": "medium", "final_answer": {"answer": 72.7285, "unit": "kPa"}, "id": "ideal_gas_000543_1.12_478_61.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.12 mol, T=478 K, and V=61.2 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 = 1.12 * 8.314 * 478 / 61.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.12, "temp_k": 478, "volume_l": 61.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=21.3 V and R=18.9 ohm.\nFinal: {\"answer\": 24.0048, \"unit\": \"W\"}", "dedupe_signature": "019d61845da82b6a167fb8c7f2a2b46a69c26b4e5bdb1f7c2ddcb2b0041a0aa1", "difficulty": "easy", "final_answer": {"answer": 24.0048, "unit": "W"}, "id": "ohm_power_000545_21.3_18.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 18.9 ohm and voltage 21.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=21.3 V and R=18.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 18.9, "voltage": 21.3}, "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 = 1165 * 0.545 * 91.\nFinal: {\"answer\": 57778.175, \"unit\": \"J\"}", "dedupe_signature": "eefc79510ed0a36952017833ea54b25e764a0e3eaa0bebe7741ed211992ecc0c", "difficulty": "easy", "final_answer": {"answer": 57778.175, "unit": "J"}, "id": "heat_q_000562_1165_0.545_91", "license": "Apache-2.0", "prompt": "A 1165 g sample has specific heat 0.545 J/(g*K). How much heat is needed to raise its temperature by 91 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1165 * 0.545 * 91.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 91, "heat_capacity": 0.545, "mass_g": 1165}, "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 = 1460 * 4.03 * 92.\nFinal: {\"answer\": 541309.6, \"unit\": \"J\"}", "dedupe_signature": "3ffa0ddcd524e048e2249e954cffd090826da2bd4b1a040ff942738f8f9d0e0a", "difficulty": "easy", "final_answer": {"answer": 541309.6, "unit": "J"}, "id": "heat_q_000580_1460_4.03_92", "license": "Apache-2.0", "prompt": "A 1460 g sample has specific heat 4.03 J/(g*K). How much heat is needed to raise its temperature by 92 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1460 * 4.03 * 92.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 92, "heat_capacity": 4.03, "mass_g": 1460}, "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=6 degrees through the sine of 2 theta.\n3. Substitute v=22.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 10.5395, \"unit\": \"m\"}", "dedupe_signature": "f24d729b2f34f6750c28110463cd033cbe3e7be7fad91da33190cff9310c7c0f", "difficulty": "medium", "final_answer": {"answer": 10.5395, "unit": "m"}, "id": "projectile_range_000596_22.3_6", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 22.3 m/s and angle 6 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=6 degrees through the sine of 2 theta.\nSubstitute v=22.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 6, "gravity": 9.81, "speed": 22.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.7 * 8.314 * 574 / 51.4.\nFinal: {\"answer\": 529.2168, \"unit\": \"kPa\"}", "dedupe_signature": "0af6d5a2fbd2e99b036d0fbc1cdef87690d6c661a046c8bf5b26f24e59b38d96", "difficulty": "medium", "final_answer": {"answer": 529.2168, "unit": "kPa"}, "id": "ideal_gas_000597_5.7_574_51.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.7 mol, T=574 K, and V=51.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.7 * 8.314 * 574 / 51.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 5.7, "temp_k": 574, "volume_l": 51.4}, "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 4625 mL to 4.625 L.\n3. Compute M = 1.22 / 4.625.\nFinal: {\"answer\": 0.2638, \"unit\": \"mol/L\"}", "dedupe_signature": "d836472013614d40a273f526cab8218692949c6fdf2ae1d929f2c706ffb4a012", "difficulty": "medium", "final_answer": {"answer": 0.2638, "unit": "mol/L"}, "id": "molarity_000602_1.22_4625", "license": "Apache-2.0", "prompt": "A solution contains 1.22 mol of solute in 4625 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4625 mL to 4.625 L.\nCompute M = 1.22 / 4.625.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.22, "volume_ml": 4625}, "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 31510.0 / 1000.\nFinal: {\"answer\": 31.51, \"unit\": \"kg\"}", "dedupe_signature": "4ca05a3f020a9428bdb640d530690f60cc54768a9100dbc93591afbe51867e9c", "difficulty": "easy", "final_answer": {"answer": 31.51, "unit": "kg"}, "id": "unit_convert_000624_g_to_kg_31510", "license": "Apache-2.0", "prompt": "Convert 31510 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 31510.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 31510.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.65, 26.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "790e58ae60918fe38973af384d73380b255f169af61c2d5af693d342e1672f33", "difficulty": "medium", "final_answer": {"answer": [9.65, 26.0], "unit": "dimensionless"}, "id": "line_two_point_000626_10.5_21_9.65_26", "license": "Apache-2.0", "prompt": "A line passes through points (10.5, 127.325) and (21, 228.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 10.5, "x2": 21.0, "y1": 127.325, "y2": 228.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "3c74b21fd7779e7f0585f0c7d02faf856b1c674bcee6c3c6dd4824efd76bd3d7", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000627_consistent_5ca82cb9_490018", "license": "Apache-2.0", "prompt": "In student derivation case 490018, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: 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": "6a62b4dbcd59a0ccc6e9ffe64cc6ae42872590b15394459fa2ca7eb88fec69a9", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000629_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing ledger records in release 808203, 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": "test", "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. 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": "0ba6386852f6ff1a79f38cde9430ef5e4e7da6659e98feb266fc38f5235e6d66", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000647_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile survey records in release 881427, 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": "test", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.6 kg and a = 7.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 41.44, \"unit\": \"N\"}", "dedupe_signature": "6080e5d34d0ee98888cff741d34e52f9a5418618d6fef5fd05b86596684c079b", "difficulty": "easy", "final_answer": {"answer": 41.44, "unit": "N"}, "id": "force_000648_5.6_7.4", "license": "Apache-2.0", "prompt": "A cart has mass 5.6 kg and measured acceleration 7.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.6 kg and a = 7.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.4, "mass": 5.6}, "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=816.5 mg, t=324.5 h, and T_half=7.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "efc371e8cd5b346d2a7af2bd2ad6e3c082e5295c868d1ad392ffdeb1bb5b1eac", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_000654_816.5_7.5_324.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 816.5 mg. Its half-life is 7.5 hours. How many mg remain after 324.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=816.5 mg, t=324.5 h, and T_half=7.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 324.5, "half_life": 7.5, "initial_amount": 816.5}, "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. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "10a4acfd9882920696595617e264bb402fa1cf79b2bf781aab9bb8aa14f22f22", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000663_inconsistent_1e14b074_567911", "license": "Apache-2.0", "prompt": "In model card equation case 567911, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.1 kg and a = 5.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 121.705, \"unit\": \"N\"}", "dedupe_signature": "5909eb0188f4944bb18c9005f1f42cb748285548417495d13e7e51d98d947bef", "difficulty": "easy", "final_answer": {"answer": 121.705, "unit": "N"}, "id": "force_000684_24.1_5.05", "license": "Apache-2.0", "prompt": "A cart has mass 24.1 kg and measured acceleration 5.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.1 kg and a = 5.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.05, "mass": 24.1}, "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 1485 mL to 1.485 L.\n3. Compute M = 4.03 / 1.485.\nFinal: {\"answer\": 2.7138, \"unit\": \"mol/L\"}", "dedupe_signature": "0b922d2f4eab1884ece74217e1ae05f5664ebb616d9c5f006b78d2fd60f710d6", "difficulty": "medium", "final_answer": {"answer": 2.7138, "unit": "mol/L"}, "id": "molarity_000710_4.03_1485", "license": "Apache-2.0", "prompt": "A solution contains 4.03 mol of solute in 1485 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1485 mL to 1.485 L.\nCompute M = 4.03 / 1.485.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.03, "volume_ml": 1485}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [-0.129, -0.218, -0.427], \"unit\": \"temperature_units\"}", "dedupe_signature": "af478bd28b22a29d2ea804c911ae95aa90b8fac5e6453b4faf7c48c27f8daa20", "difficulty": "hard", "final_answer": {"answer": [-0.129, -0.218, -0.427], "unit": "temperature_units"}, "id": "heat_step_000713_0.06_2.45_-0.3_-0.2_-0.4_-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=2.45, right=-1.05; current interior values are [-0.3, -0.2, -0.4]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.3, -0.2, -0.4], "left": 2.45, "r": 0.06, "right": -1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"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 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "89d74ed1bd47664b02f95bd04227cca3de38597d3c2eb5f0dc539a16b85eb7ec", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000729_59_0.65_1.3_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.65 y with y(0)=59, step size h=1.3, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 59.0, "rate": 0.65, "step": 1.3, "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=55.5 mg, t=85.5 h, and T_half=108 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 32.061, \"unit\": \"mg\"}", "dedupe_signature": "ea518719b0f87f0216766b8a981947aa10ad32c35c45b94f54db04dec11703aa", "difficulty": "medium", "final_answer": {"answer": 32.061, "unit": "mg"}, "id": "half_life_000744_55.5_108_85.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 55.5 mg. Its half-life is 108 hours. How many mg remain after 85.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=55.5 mg, t=85.5 h, and T_half=108 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 85.5, "half_life": 108.0, "initial_amount": 55.5}, "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: 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": "5bf67f7e59820f69aba815a65daeb6b4ccb02c61d73617f75fc43869e3dca4b0", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_000755_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry experiment record from batch 728106 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": "test", "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) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "e30f787f677efaa9b32c5f1ec2aba0897d851905479c3d6dfd41bca447650137", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000765_8_0.63_1.5_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=8, step size h=1.5, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 8.0, "rate": 0.63, "step": 1.5, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [-0.76, -0.73, 0.727], \"unit\": \"temperature_units\"}", "dedupe_signature": "fdb2ae1bbad2c39f7ea8f8d0610d6be758cedbc228d7fc7bb9e6095142b98a2a", "difficulty": "hard", "final_answer": {"answer": [-0.76, -0.73, 0.727], "unit": "temperature_units"}, "id": "heat_step_000767_0.06_-1.55_-0.7_-0.85_1.0_-1.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.55, right=-1.7; current interior values are [-0.7, -0.85, 1.0]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.7, -0.85, 1.0], "left": -1.55, "r": 0.06, "right": -1.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 103.5 + 273.15.\nFinal: {\"answer\": 376.65, \"unit\": \"K\"}", "dedupe_signature": "f572967b7fe7d7b684db6b7055abd3606a48a846abe356f3f2bcb90ca30e331e", "difficulty": "easy", "final_answer": {"answer": 376.65, "unit": "K"}, "id": "unit_convert_000768_c_to_k_103.5", "license": "Apache-2.0", "prompt": "Convert 103.5 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 103.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 103.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=7 degrees and keep the unit as newtons.\nFinal: {\"answer\": [199.5018, 24.4957], \"unit\": \"N\"}", "dedupe_signature": "67e55fec7e404f0af1882019960be0fdb2a905f842a970000df7706e3867e6c2", "difficulty": "medium", "final_answer": {"answer": [199.5018, 24.4957], "unit": "N"}, "id": "vector_components_000769_201_7", "license": "Apache-2.0", "prompt": "A vector has magnitude 201 N at 7 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=7 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 7, "magnitude": 201.0}, "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 = 1585 * 3.755 * 62.\nFinal: {\"answer\": 369003.85, \"unit\": \"J\"}", "dedupe_signature": "70b7b39ee5b71293a6548623924a1a68b433ebf9f8299637f7fd54ec0579af2d", "difficulty": "easy", "final_answer": {"answer": 369003.85, "unit": "J"}, "id": "heat_q_000778_1585_3.755_62", "license": "Apache-2.0", "prompt": "A 1585 g sample has specific heat 3.755 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 = 1585 * 3.755 * 62.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 62, "heat_capacity": 3.755, "mass_g": 1585}, "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: 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": "6ca2388dc98a180e653d07d9bd65236bc1eba86adc08f235088574ec545b31c2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000791_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 [1.6, -0.75, -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": "test", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.15 kg and a = 3.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 95.3925, \"unit\": \"N\"}", "dedupe_signature": "657c85692f4d32fa40acfef172c1a8344a69a5d299eddf5d58f114c76e102988", "difficulty": "easy", "final_answer": {"answer": 95.3925, "unit": "N"}, "id": "force_000792_24.15_3.95", "license": "Apache-2.0", "prompt": "A cart has mass 24.15 kg and measured acceleration 3.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.15 kg and a = 3.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.95, "mass": 24.15}, "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 = 1.24 * 8.314 * 276 / 114.8.\nFinal: {\"answer\": 24.7856, \"unit\": \"kPa\"}", "dedupe_signature": "944eadcbb38e795ca3db2c75fbcda7ffac32f50455fbaba81424f83c75cf3542", "difficulty": "medium", "final_answer": {"answer": 24.7856, "unit": "kPa"}, "id": "ideal_gas_000813_1.24_276_114.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.24 mol, T=276 K, and V=114.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.24 * 8.314 * 276 / 114.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.24, "temp_k": 276, "volume_l": 114.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 630 mL to 0.63 L.\n3. Compute M = 0.075 / 0.63.\nFinal: {\"answer\": 0.119, \"unit\": \"mol/L\"}", "dedupe_signature": "93b6a2baf5387bca16292b24db8f66b3ecf1550304aac3fb91ffd18ffe9cfdc8", "difficulty": "medium", "final_answer": {"answer": 0.119, "unit": "mol/L"}, "id": "molarity_000818_0.075_630", "license": "Apache-2.0", "prompt": "A solution contains 0.075 mol of solute in 630 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 630 mL to 0.63 L.\nCompute M = 0.075 / 0.63.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 0.075, "volume_ml": 630}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.8)=-78.86 and f(-6.1)=-52.22.\n3. The interval width is 3.7.\nFinal: {\"answer\": -242.498, \"unit\": \"area_units\"}", "dedupe_signature": "eea652d522739f303ef7ad2a6a77543612037adce5bc427e03e887a8fbd140bf", "difficulty": "medium", "final_answer": {"answer": -242.498, "unit": "area_units"}, "id": "trapz_linear_000820_7.2_-8.3_-9.8_-6.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.2x+-8.3 from x=-9.8 to x=-6.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.8)=-78.86 and f(-6.1)=-52.22.\nThe interval width is 3.7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -8.3, "slope": 7.2, "x0": -9.8, "x1": -6.1000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [-1.66, -1.245, -0.145], \"unit\": \"temperature_units\"}", "dedupe_signature": "6cf57096398df018b17f4105fd50e3b013a81b7b4204c708d673053abe983f6d", "difficulty": "hard", "final_answer": {"answer": [-1.66, -1.245, -0.145], "unit": "temperature_units"}, "id": "heat_step_000821_0.1_0.7_-2.0_-1.3_-0.05_0.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=0.25; current interior values are [-2.0, -1.3, -0.05]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-2.0, -1.3, -0.05], "left": 0.7, "r": 0.1, "right": 0.25}, "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 finite_differences_000826(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_000826\"}", "dedupe_signature": "934d230e333247f118a829275a90fd99e29b6bc1ae1cf1c840757bcdb72b8ca8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_000826"}, "id": "code_000826_finite_differences_000826", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_000826(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": "test", "task_family": "python_code_generation", "variables": {"function": "finite_differences_000826"}, "verifier": {"function": "finite_differences_000826", "tests": ["assert finite_differences_000826([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_000826([5]) == []", "assert finite_differences_000826([]) == []"], "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=37 degrees through the sine of 2 theta.\n3. Substitute v=54.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 291.0487, \"unit\": \"m\"}", "dedupe_signature": "8e7808ab19d34af6a46598e57df07bad64740b30c3d25cf14f419ed54555a655", "difficulty": "medium", "final_answer": {"answer": 291.0487, "unit": "m"}, "id": "projectile_range_000830_54.5_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=37 degrees through the sine of 2 theta.\nSubstitute v=54.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 54.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 995 * 1.705 * 34.\nFinal: {\"answer\": 57680.15, \"unit\": \"J\"}", "dedupe_signature": "128568924f81c102c84562cdbf87b650f102d427f43f588e5ab2175d1224553f", "difficulty": "easy", "final_answer": {"answer": 57680.15, "unit": "J"}, "id": "heat_q_000832_995_1.705_34", "license": "Apache-2.0", "prompt": "A 995 g sample has specific heat 1.705 J/(g*K). How much heat is needed to raise its temperature by 34 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 995 * 1.705 * 34.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 34, "heat_capacity": 1.705, "mass_g": 995}, "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 weighted_sum_000844(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_000844\"}", "dedupe_signature": "6ea0c55c5949b3dcbc12d3d14caf710a55de9a7210c58dac5607e260395554f2", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000844"}, "id": "code_000844_weighted_sum_000844", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000844(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": "test", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000844"}, "verifier": {"function": "weighted_sum_000844", "tests": ["assert weighted_sum_000844([2, 3], [4, 5]) == 23", "assert weighted_sum_000844([], []) == 0", "try:\n    weighted_sum_000844([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"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 1540.0 / 100.\nFinal: {\"answer\": 15.4, \"unit\": \"m\"}", "dedupe_signature": "e809f863a1d07aaac41cd06aa15024ead7454c5637b2863472c3205ee9838499", "difficulty": "easy", "final_answer": {"answer": 15.4, "unit": "m"}, "id": "unit_convert_000858_cm_to_m_1540", "license": "Apache-2.0", "prompt": "Convert 1540 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 1540.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 1540.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=318 degrees and keep the unit as newtons.\nFinal: {\"answer\": [23.4091, -21.0776], \"unit\": \"N\"}", "dedupe_signature": "2b2e8dbbf914cf017ae8918e0dd8067209a618703e925c8ff62e3b85e1d74ec7", "difficulty": "medium", "final_answer": {"answer": [23.4091, -21.0776], "unit": "N"}, "id": "vector_components_000859_31.5_318", "license": "Apache-2.0", "prompt": "A vector has magnitude 31.5 N at 318 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=318 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 318, "magnitude": 31.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.3, -26.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0f8b1f6a2b36d4c104fd25eff9b259869d67008f4e555f3829d526b40d069379", "difficulty": "medium", "final_answer": {"answer": [4.3, -26.75], "unit": "dimensionless"}, "id": "line_two_point_000860_9_20.75_4.3_-26.75", "license": "Apache-2.0", "prompt": "A line passes through points (9, 11.95) and (20.75, 62.475). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 9.0, "x2": 20.75, "y1": 11.949999999999996, "y2": 62.474999999999994}, "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 x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=291 degrees and keep the unit as newtons.\nFinal: {\"answer\": [94.0716, -245.0649], \"unit\": \"N\"}", "dedupe_signature": "e8d09d4852a748a2b1a57da22e13ae8cd90b80d9cb63ae7ffb9c14e6198e861b", "difficulty": "medium", "final_answer": {"answer": [94.0716, -245.0649], "unit": "N"}, "id": "vector_components_000877_262.5_291", "license": "Apache-2.0", "prompt": "A vector has magnitude 262.5 N at 291 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=291 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 291, "magnitude": 262.5}, "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. Mass equals amount in moles times molar mass.\n2. Use m = 1.21 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 21.7981, \"unit\": \"g\"}", "dedupe_signature": "472ddeda081409c01ac00ac8608e19da5e452a6f4ca3f33a2ad5a41fbd029e65", "difficulty": "medium", "final_answer": {"answer": 21.7981, "unit": "g"}, "id": "stoich_mass_000889_water_1.21", "license": "Apache-2.0", "prompt": "A sample contains 1.21 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.21 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.21}, "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 = 1.67 * 8.314 * 546 / 109.1.\nFinal: {\"answer\": 69.4855, \"unit\": \"kPa\"}", "dedupe_signature": "d29a296fc5d69c9b9d0dbb65758ca5892c1279674790bd139d142da4d2ad161a", "difficulty": "medium", "final_answer": {"answer": 69.4855, "unit": "kPa"}, "id": "ideal_gas_000903_1.67_546_109.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.67 mol, T=546 K, and V=109.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.67 * 8.314 * 546 / 109.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.67, "temp_k": 546, "volume_l": 109.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=123 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-98.5797, 151.7994], \"unit\": \"N\"}", "dedupe_signature": "7592725a322b7d88d272a05744502edb6d3e0f397e422e2bb0809896c74d39d2", "difficulty": "medium", "final_answer": {"answer": [-98.5797, 151.7994], "unit": "N"}, "id": "vector_components_000931_181_123", "license": "Apache-2.0", "prompt": "A vector has magnitude 181 N at 123 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=123 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 123, "magnitude": 181.0}, "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_000934(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_000934\"}", "dedupe_signature": "e2676b86ad7c501c6d546815516ce9c48ba577d21c3c8f4d75c1191a1de0e175", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_000934"}, "id": "code_000934_normalize_000934", "license": "Apache-2.0", "prompt": "Write a Python function normalize_000934(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": "test", "task_family": "python_code_generation", "variables": {"function": "normalize_000934"}, "verifier": {"function": "normalize_000934", "tests": ["out = normalize_000934([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_000934([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_000934([1, 1]) == [0.5, 0.5]", "try:\n    normalize_000934([1, -1])\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 = 4.96 * 8.314 * 241 / 93.3.\nFinal: {\"answer\": 106.519, \"unit\": \"kPa\"}", "dedupe_signature": "1c889d3d87f5a069c2175b09c3df40746b26bcf411ed4201592dcda6f89d2f68", "difficulty": "medium", "final_answer": {"answer": 106.519, "unit": "kPa"}, "id": "ideal_gas_000939_4.96_241_93.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.96 mol, T=241 K, and V=93.3 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 = 4.96 * 8.314 * 241 / 93.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.96, "temp_k": 241, "volume_l": 93.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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 28.0 + 273.15.\nFinal: {\"answer\": 301.15, \"unit\": \"K\"}", "dedupe_signature": "0721a48446fc74138fdce33c06da1466fc48e10b2a75e24cb0c8ba2fd8f1b71c", "difficulty": "easy", "final_answer": {"answer": 301.15, "unit": "K"}, "id": "unit_convert_000948_c_to_k_28", "license": "Apache-2.0", "prompt": "Convert 28 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 28.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 28.0}, "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 = 23.4^2 and multiply by 0.5 * 21.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5831.514, \"unit\": \"J\"}", "dedupe_signature": "96f15884d21c9943f44eb520694040dbd6dd80ba76667bd8cc5bb8573dbaa7af", "difficulty": "easy", "final_answer": {"answer": 5831.514, "unit": "J"}, "id": "ke_000973_21.3_23.4", "license": "Apache-2.0", "prompt": "A body of mass 21.3 kg moves at 23.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.4^2 and multiply by 0.5 * 21.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.3, "velocity": 23.4}, "verifier": {"formula": "0.5 * mass * velocity ** 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: 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": "86947e0cd287fcd76e5c7b61ca7693588d673f4cbe1cacd2330fc7def11cb782", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000989_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry survey records in release 360149, 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": "test", "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. Mass equals amount in moles times molar mass.\n2. Use m = 4.06 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 731.4334, \"unit\": \"g\"}", "dedupe_signature": "5199e131d949d43537a3a3233b2fda15465e184cb03159d91018914e4ca71649", "difficulty": "medium", "final_answer": {"answer": 731.4334, "unit": "g"}, "id": "stoich_mass_000997_glucose_4.06", "license": "Apache-2.0", "prompt": "A sample contains 4.06 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.06 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.06}, "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 = 5.46 * 8.314 * 342 / 115.3.\nFinal: {\"answer\": 134.6479, \"unit\": \"kPa\"}", "dedupe_signature": "eafdf47250dba8dd09b6dd181125d24cb5c376ac387845f955026a39f973e3af", "difficulty": "medium", "final_answer": {"answer": 134.6479, "unit": "kPa"}, "id": "ideal_gas_001011_5.46_342_115.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.46 mol, T=342 K, and V=115.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.46 * 8.314 * 342 / 115.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 5.46, "temp_k": 342, "volume_l": 115.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 390 * 0.53 * 41.\nFinal: {\"answer\": 8474.7, \"unit\": \"J\"}", "dedupe_signature": "a33376ebb8adee4113af32fee0e366bb44871314c7986bbe7c4650aaa2a60169", "difficulty": "easy", "final_answer": {"answer": 8474.7, "unit": "J"}, "id": "heat_q_001012_390_0.53_41", "license": "Apache-2.0", "prompt": "A 390 g sample has specific heat 0.53 J/(g*K). How much heat is needed to raise its temperature by 41 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 390 * 0.53 * 41.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 41, "heat_capacity": 0.53, "mass_g": 390}, "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=82 mg, t=12 h, and T_half=2.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 2.9435, \"unit\": \"mg\"}", "dedupe_signature": "287e22ebb9f50cc6a2c6bb121017cafbd828a9695fa53ba81a2c21b62adbd2c3", "difficulty": "medium", "final_answer": {"answer": 2.9435, "unit": "mg"}, "id": "half_life_001014_82_2.5_12", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 82 mg. Its half-life is 2.5 hours. How many mg remain after 12 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=82 mg, t=12 h, and T_half=2.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 12.0, "half_life": 2.5, "initial_amount": 82.0}, "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. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b92cabaf07923e6e629472c655efa6f7693c8e99bb4b145b2053ef3c81ec60ff", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001041_consistent_82e93f3d_548293", "license": "Apache-2.0", "prompt": "In lab notebook case 548293, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "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=131 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-27.8825, 32.0752], \"unit\": \"N\"}", "dedupe_signature": "293cea36d6fbde8ad5f59cc13b71acfaf65ca3b77a7759e1f91a4b739850fc2c", "difficulty": "medium", "final_answer": {"answer": [-27.8825, 32.0752], "unit": "N"}, "id": "vector_components_001057_42.5_131", "license": "Apache-2.0", "prompt": "A vector has magnitude 42.5 N at 131 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=131 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 131, "magnitude": 42.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "caafce535a9812dc7913b3d788af6f53af831d563b678da27fd811819f2162ac", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001059_consistent_82e93f3d_616841", "license": "Apache-2.0", "prompt": "In simulation spec case 616841, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "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=115 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-130.589, 280.0491], \"unit\": \"N\"}", "dedupe_signature": "709f10fa9b39a0e78340c4012f850a7cffbbf637c62c4cf745d6de2731546cbd", "difficulty": "medium", "final_answer": {"answer": [-130.589, 280.0491], "unit": "N"}, "id": "vector_components_001075_309_115", "license": "Apache-2.0", "prompt": "A vector has magnitude 309 N at 115 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=115 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 115, "magnitude": 309.0}, "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 = 5.87 * 8.314 * 373 / 17.8.\nFinal: {\"answer\": 1022.6734, \"unit\": \"kPa\"}", "dedupe_signature": "420271005ee46c695db16ea6190d0f465087eddd0cb7beb2b26a0fa3ce9ff3fa", "difficulty": "medium", "final_answer": {"answer": 1022.6734, "unit": "kPa"}, "id": "ideal_gas_001083_5.87_373_17.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.87 mol, T=373 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 = 5.87 * 8.314 * 373 / 17.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 5.87, "temp_k": 373, "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. Mass equals amount in moles times molar mass.\n2. Use m = 0.97 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 97.0844, \"unit\": \"g\"}", "dedupe_signature": "8d9b982b0648bc7534c4bbb8ff137aa4d0ea8293e3cf93a207d0b10f22d13a42", "difficulty": "medium", "final_answer": {"answer": 97.0844, "unit": "g"}, "id": "stoich_mass_001087_calcium_carbonate_0.97", "license": "Apache-2.0", "prompt": "A sample contains 0.97 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.97 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.97}, "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\nimport math\n\ndef unit_vector_001096(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_001096\"}", "dedupe_signature": "e1c464e531cdc6ebbecc06dc83aa9585c7d12d54452dbefc3e4397a1026f3f57", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001096"}, "id": "code_001096_unit_vector_001096", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001096(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": "test", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001096"}, "verifier": {"function": "unit_vector_001096", "tests": ["ux, uy = unit_vector_001096(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001096(0, 5) == (0, 1)", "try:\n    unit_vector_001096(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "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 6 steps and round the final state.\nFinal: {\"answer\": 2.3764, \"unit\": \"state_units\"}", "dedupe_signature": "e29e156b2f7ad1774257692e40305416e8b85c8f914ac8d92c6e89701a037ed7", "difficulty": "medium", "final_answer": {"answer": 2.3764, "unit": "state_units"}, "id": "euler_decay_001107_16.5_0.69_0.4_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.69 y with y(0)=16.5, step size h=0.4, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 16.5, "rate": 0.69, "step": 0.4, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3185 mL to 3.185 L.\n3. Compute M = 4.875 / 3.185.\nFinal: {\"answer\": 1.5306, \"unit\": \"mol/L\"}", "dedupe_signature": "60e6c4a42295462ee841d1e79bfb455b12eeed521b08f529d067806ae9acdada", "difficulty": "medium", "final_answer": {"answer": 1.5306, "unit": "mol/L"}, "id": "molarity_001124_4.875_3185", "license": "Apache-2.0", "prompt": "A solution contains 4.875 mol of solute in 3185 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3185 mL to 3.185 L.\nCompute M = 4.875 / 3.185.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.875, "volume_ml": 3185}, "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 safe_mean_001132(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_001132\"}", "dedupe_signature": "eb1cfe635a94df0fc462e763c46cc603e3a4cb6fee1577539676a3600b901b4f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001132"}, "id": "code_001132_safe_mean_001132", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001132(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001132"}, "verifier": {"function": "safe_mean_001132", "tests": ["assert safe_mean_001132([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001132(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001132([])\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(1.7)=14.88 and f(7.6)=11.34.\n3. The interval width is 5.9.\nFinal: {\"answer\": 77.349, \"unit\": \"area_units\"}", "dedupe_signature": "e24f176f6daf553559c8e24dec4759a94bdbbf0237773e992acfdd5075482349", "difficulty": "medium", "final_answer": {"answer": 77.349, "unit": "area_units"}, "id": "trapz_linear_001144_-0.6_15.9_1.7_7.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+15.9 from x=1.7 to x=7.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.7)=14.88 and f(7.6)=11.34.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 15.9, "slope": -0.6, "x0": 1.7, "x1": 7.6000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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=61.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 66.5154, \"unit\": \"m\"}", "dedupe_signature": "d69daa8cda4d03a1c44be1706e4b815296e91ed6bf595b8280ee572c1a2980c9", "difficulty": "medium", "final_answer": {"answer": 66.5154, "unit": "m"}, "id": "projectile_range_001154_61.3_85", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.3 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=61.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 85, "gravity": 9.81, "speed": 61.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.58 * 8.314 * 501 / 3.0.\nFinal: {\"answer\": 3582.17, \"unit\": \"kPa\"}", "dedupe_signature": "7d7c666b8aef8338b202d50f1d300499340fb66b10674175ceed333463590ab4", "difficulty": "medium", "final_answer": {"answer": 3582.17, "unit": "kPa"}, "id": "ideal_gas_001173_2.58_501_3.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.58 mol, T=501 K, and V=3.0 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 = 2.58 * 8.314 * 501 / 3.0.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.58, "temp_k": 501, "volume_l": 3.0}, "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(-7.8)=-19.66 and f(-1.9)=5.12.\n3. The interval width is 5.9.\nFinal: {\"answer\": -42.893, \"unit\": \"area_units\"}", "dedupe_signature": "3e317c48f360578509656ac282efdae67a2bff5402f1ab5dfe369bdfd05ea5ea", "difficulty": "medium", "final_answer": {"answer": -42.893, "unit": "area_units"}, "id": "trapz_linear_001180_4.2_13.1_-7.8_-1.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.2x+13.1 from x=-7.8 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(-7.8)=-19.66 and f(-1.9)=5.12.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 13.1, "slope": 4.2, "x0": -7.8, "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. 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\": [57.9117, 328.4334], \"unit\": \"N\"}", "dedupe_signature": "9bf31cead554603d68a98a02d25af9728feea3f7bd35bad89668fb5c7ff42280", "difficulty": "medium", "final_answer": {"answer": [57.9117, 328.4334], "unit": "N"}, "id": "vector_components_001183_333.5_80", "license": "Apache-2.0", "prompt": "A vector has magnitude 333.5 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": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 80, "magnitude": 333.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "ad0660c70359d750ee6d938f547c22fdc453708090e4ceaf6d6c4cea9e966849", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001187_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each warehouse clinical record from batch 745578 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": "test", "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. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.156, 2.588, 2.008], \"unit\": \"temperature_units\"}", "dedupe_signature": "d571eec8c551922721665814f477c1423e45525db31436dc25ce4e6318397ff5", "difficulty": "hard", "final_answer": {"answer": [-0.156, 2.588, 2.008], "unit": "temperature_units"}, "id": "heat_step_001199_0.08_-0.65_-0.4_2.9_2.3_-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=-0.65, right=-1.95; current interior values are [-0.4, 2.9, 2.3]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.4, 2.9, 2.3], "left": -0.65, "r": 0.08, "right": -1.95}, "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 = 5.23 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 942.2159, \"unit\": \"g\"}", "dedupe_signature": "3cd11da71bbeda0b38bcbe782c871e0a05fc925ddd8046bc0f378c4aae7305c8", "difficulty": "medium", "final_answer": {"answer": 942.2159, "unit": "g"}, "id": "stoich_mass_001213_glucose_5.23", "license": "Apache-2.0", "prompt": "A sample contains 5.23 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.23 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.23}, "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=212.1 V and R=129.9 ohm.\nFinal: {\"answer\": 346.3157, \"unit\": \"W\"}", "dedupe_signature": "4b796d6c759edd15cd62d8755982d4d2200893869561264028758b5e3e8fa756", "difficulty": "easy", "final_answer": {"answer": 346.3157, "unit": "W"}, "id": "ohm_power_001229_212.1_129.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 129.9 ohm and voltage 212.1 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=212.1 V and R=129.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 129.9, "voltage": 212.1}, "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 = 5.62 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 562.4889, \"unit\": \"g\"}", "dedupe_signature": "79fa90083b7f10aa399c55b1cff070e084d921d4b1fb4b0a3d03bc3a55beb295", "difficulty": "medium", "final_answer": {"answer": 562.4889, "unit": "g"}, "id": "stoich_mass_001231_calcium_carbonate_5.62", "license": "Apache-2.0", "prompt": "A sample contains 5.62 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.62 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.62}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.85 kg and a = 13.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 50.82, \"unit\": \"N\"}", "dedupe_signature": "6314f157c8531e325f741c510e8461667282069d43c816ec397fd91777b4379b", "difficulty": "easy", "final_answer": {"answer": 50.82, "unit": "N"}, "id": "force_001242_3.85_13.2", "license": "Apache-2.0", "prompt": "A cart has mass 3.85 kg and measured acceleration 13.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.85 kg and a = 13.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.2, "mass": 3.85}, "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 = 4.2 kg and a = 12.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.92, \"unit\": \"N\"}", "dedupe_signature": "425d395fb1ae44e8aabd57c215ab6febc89bd7d56a5ca94c9af26048a1ef8530", "difficulty": "easy", "final_answer": {"answer": 52.92, "unit": "N"}, "id": "force_001260_4.2_12.6", "license": "Apache-2.0", "prompt": "A cart has mass 4.2 kg and measured acceleration 12.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.2 kg and a = 12.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.6, "mass": 4.2}, "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=0.3 and add it to the current value.\nFinal: {\"answer\": [0.48, -0.12, -0.325], \"unit\": \"temperature_units\"}", "dedupe_signature": "5e5d66e0eab62919d861646095cd531db56fdc867723df141c2e7c388ddb3a1d", "difficulty": "hard", "final_answer": {"answer": [0.48, -0.12, -0.325], "unit": "temperature_units"}, "id": "heat_step_001271_0.3_-1.05_3.0_-1.35_-1.6_2.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.05, right=2.4; current interior values are [3.0, -1.35, -1.6]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [3.0, -1.35, -1.6], "left": -1.05, "r": 0.3, "right": 2.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=91 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-5.5237, 316.4518], \"unit\": \"N\"}", "dedupe_signature": "6b2def56e238022f3e73da3eadb02b23410766f6f356cab44468dc561c6193ba", "difficulty": "medium", "final_answer": {"answer": [-5.5237, 316.4518], "unit": "N"}, "id": "vector_components_001273_316.5_91", "license": "Apache-2.0", "prompt": "A vector has magnitude 316.5 N at 91 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=91 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 91, "magnitude": 316.5}, "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 the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.94 * 8.314 * 241 / 5.5.\nFinal: {\"answer\": 1071.0548, \"unit\": \"kPa\"}", "dedupe_signature": "785e2ada33fc1520e469897f3a57c26eca56d1615904d53a399f88bc8dcfb11e", "difficulty": "medium", "final_answer": {"answer": 1071.0548, "unit": "kPa"}, "id": "ideal_gas_001281_2.94_241_5.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.94 mol, T=241 K, and V=5.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.94 * 8.314 * 241 / 5.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.94, "temp_k": 241, "volume_l": 5.5}, "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=491.5 mg, t=310 h, and T_half=3.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "b8ee018c22f1275475176df1994532950f2fc2d6dc8f4bcdd1d2e27c0bba3b70", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_001284_491.5_3.5_310", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 491.5 mg. Its half-life is 3.5 hours. How many mg remain after 310 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=491.5 mg, t=310 h, and T_half=3.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 310.0, "half_life": 3.5, "initial_amount": 491.5}, "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 * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 410.2488, \"unit\": \"g\"}", "dedupe_signature": "7052ba1a2349814cac2b9a782edd30cff85e1098908a3374080d0a6807e80c25", "difficulty": "medium", "final_answer": {"answer": 410.2488, "unit": "g"}, "id": "stoich_mass_001285_sodium_chloride_7.02", "license": "Apache-2.0", "prompt": "A sample contains 7.02 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.02 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.02}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.95 kg and a = 12.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 192.995, \"unit\": \"N\"}", "dedupe_signature": "bb8ad1ca4ba1f2e9299cef4b5dade441adbcdf39ef164416a2d0bc80059c23e5", "difficulty": "easy", "final_answer": {"answer": 192.995, "unit": "N"}, "id": "force_001296_15.95_12.1", "license": "Apache-2.0", "prompt": "A cart has mass 15.95 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.95 kg and a = 12.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.1, "mass": 15.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 40^2 and multiply by 0.5 * 28.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 22680.0, \"unit\": \"J\"}", "dedupe_signature": "df9045e1fb1076c26eb19d2c991c5b1d138d71133e197e1eb7556de18d9b4e10", "difficulty": "easy", "final_answer": {"answer": 22680.0, "unit": "J"}, "id": "ke_001297_28.35_40", "license": "Apache-2.0", "prompt": "A body of mass 28.35 kg moves at 40 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 40^2 and multiply by 0.5 * 28.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.35, "velocity": 40.0}, "verifier": {"formula": "0.5 * mass * velocity ** 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": "00d2362a81fe359b0c8e94e2c69a0834f39cf43f2a7a293399853267c44d2f05", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001313_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each billing experiment record from batch 70994 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": "test", "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 = 1.79 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 32.2469, \"unit\": \"g\"}", "dedupe_signature": "158dd09fcbbf7d57cc6b5e943f31fe11589c0c23eb02fa11ccf1ce6f39cfa4e1", "difficulty": "medium", "final_answer": {"answer": 32.2469, "unit": "g"}, "id": "stoich_mass_001321_water_1.79", "license": "Apache-2.0", "prompt": "A sample contains 1.79 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.79 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.79}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.4)=-4.26 and f(16.4)=-21.36.\n3. The interval width is 9.\nFinal: {\"answer\": -115.29, \"unit\": \"area_units\"}", "dedupe_signature": "6adb293748a69af92aba70e675ef0dcae0e34800c4da31cb347d1c49e76e2886", "difficulty": "medium", "final_answer": {"answer": -115.29, "unit": "area_units"}, "id": "trapz_linear_001324_-1.9_9.8_7.4_16.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+9.8 from x=7.4 to x=16.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.4)=-4.26 and f(16.4)=-21.36.\nThe interval width is 9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 9.8, "slope": -1.9, "x0": 7.4, "x1": 16.4}, "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\": [3.65, -5.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "27a579088c1427721ce33c09ed7642c422dcde8462be83006c787597fa104e65", "difficulty": "medium", "final_answer": {"answer": [3.65, -5.75], "unit": "dimensionless"}, "id": "line_two_point_001328_-8.75_6.25_3.65_-5.75", "license": "Apache-2.0", "prompt": "A line passes through points (-8.75, -37.6875) and (6.25, 17.0625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -8.75, "x2": 6.25, "y1": -37.6875, "y2": 17.0625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 2.15^2 and multiply by 0.5 * 28.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 66.3329, \"unit\": \"J\"}", "dedupe_signature": "d8c10fce8fb0193557ff12f03477f459f61b2c2f139fce848b9220163efc0cd7", "difficulty": "easy", "final_answer": {"answer": 66.3329, "unit": "J"}, "id": "ke_001333_28.7_2.15", "license": "Apache-2.0", "prompt": "A body of mass 28.7 kg moves at 2.15 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 = 2.15^2 and multiply by 0.5 * 28.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.7, "velocity": 2.15}, "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=60.1 V and R=192.8 ohm.\nFinal: {\"answer\": 18.7345, \"unit\": \"W\"}", "dedupe_signature": "7fedb179eb8e113f4bda3544563164f4a9ac391e519c2679251c7bd43e57d1e4", "difficulty": "easy", "final_answer": {"answer": 18.7345, "unit": "W"}, "id": "ohm_power_001337_60.1_192.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 192.8 ohm and voltage 60.1 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=60.1 V and R=192.8 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 192.8, "voltage": 60.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.54 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 440.6376, \"unit\": \"g\"}", "dedupe_signature": "681e1c0b1641aac48ce01fe3c153fee529e772a1b05274452c862a67c857fee8", "difficulty": "medium", "final_answer": {"answer": 440.6376, "unit": "g"}, "id": "stoich_mass_001339_sodium_chloride_7.54", "license": "Apache-2.0", "prompt": "A sample contains 7.54 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.54 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.54}, "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=0.4 and add it to the current value.\nFinal: {\"answer\": [0.78, -0.44, -0.33], \"unit\": \"temperature_units\"}", "dedupe_signature": "4f7acf1bf8d46ce8697af9c56c675c71bbb5cc205362d3adfff64b1dbea7a547", "difficulty": "hard", "final_answer": {"answer": [0.78, -0.44, -0.33], "unit": "temperature_units"}, "id": "heat_step_001343_0.4_1.7_-1.3_0.9_-0.25_-1.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=-1.6; current interior values are [-1.3, 0.9, -0.25]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.3, 0.9, -0.25], "left": 1.7, "r": 0.4, "right": -1.6}, "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 = 15.25 kg and a = 12.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 185.2875, \"unit\": \"N\"}", "dedupe_signature": "7c038990a1b16ca6212e99a3b66aff7aec9dcdeeda8f6cf0d393de93b8163391", "difficulty": "easy", "final_answer": {"answer": 185.2875, "unit": "N"}, "id": "force_001350_15.25_12.15", "license": "Apache-2.0", "prompt": "A cart has mass 15.25 kg and measured acceleration 12.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.25 kg and a = 12.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.15, "mass": 15.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.1^2 and multiply by 0.5 * 10.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5029.492, \"unit\": \"J\"}", "dedupe_signature": "cbee328876efa98aa4d8aab9e187c19e3032f7bb6ef1735b20d63053c91b4fbf", "difficulty": "easy", "final_answer": {"answer": 5029.492, "unit": "J"}, "id": "ke_001351_10.4_31.1", "license": "Apache-2.0", "prompt": "A body of mass 10.4 kg moves at 31.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.1^2 and multiply by 0.5 * 10.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.4, "velocity": 31.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 193.0 + 273.15.\nFinal: {\"answer\": 466.15, \"unit\": \"K\"}", "dedupe_signature": "dfb3424b34f22d701805a7b267083824f8d92082d811788d78029fb2c07d3e92", "difficulty": "easy", "final_answer": {"answer": 466.15, "unit": "K"}, "id": "unit_convert_001362_c_to_k_193", "license": "Apache-2.0", "prompt": "Convert 193 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 193.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 193.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=17.9 V and R=84.1 ohm.\nFinal: {\"answer\": 3.8099, \"unit\": \"W\"}", "dedupe_signature": "8617dcc09fdf3f04ac6ac74fec833e64c2e6fc8e3af0e748f34f6683ff2ef891", "difficulty": "easy", "final_answer": {"answer": 3.8099, "unit": "W"}, "id": "ohm_power_001373_17.9_84.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 84.1 ohm and voltage 17.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=17.9 V and R=84.1 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 84.1, "voltage": 17.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=644.5 mg, t=119 h, and T_half=60 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 162.9972, \"unit\": \"mg\"}", "dedupe_signature": "6a39d81bc5f0c3ec8fd72163c83d18add483e6daaccc892a0035d20b6cc4d43c", "difficulty": "medium", "final_answer": {"answer": 162.9972, "unit": "mg"}, "id": "half_life_001374_644.5_60_119", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 644.5 mg. Its half-life is 60 hours. How many mg remain after 119 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=644.5 mg, t=119 h, and T_half=60 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 119.0, "half_life": 60.0, "initial_amount": 644.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, 5.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "9ad1a0a354f9f7dc3108694525d62133ccf851a78d6f5ebdc28d1b4659eaff3b", "difficulty": "medium", "final_answer": {"answer": [-4.55, 5.75], "unit": "dimensionless"}, "id": "line_two_point_001382_1.75_2.25_-4.55_5.75", "license": "Apache-2.0", "prompt": "A line passes through points (1.75, -2.2125) and (2.25, -4.4875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 1.75, "x2": 2.25, "y1": -2.2124999999999995, "y2": -4.487499999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "fe48f9a2654e09c3038e27f403ccc546ee3ff8d42252dcce1f7a7fbe1a23f101", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001385_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field sensor record from batch 91633 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": "test", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=27 degrees through the sine of 2 theta.\n3. Substitute v=24.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 47.8986, \"unit\": \"m\"}", "dedupe_signature": "2baa8950e1aed6c5d0d36bccf1e7a1ad99d05c5dc0a4596334d9f0a1379e2234", "difficulty": "medium", "final_answer": {"answer": 47.8986, "unit": "m"}, "id": "projectile_range_001388_24.1_27", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 24.1 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=27 degrees through the sine of 2 theta.\nSubstitute v=24.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 27, "gravity": 9.81, "speed": 24.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=631 mg, t=320 h, and T_half=14 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0001, \"unit\": \"mg\"}", "dedupe_signature": "5c8ce604fb19dfdede583d402c49c1e15a3e793703c20954354e72660dc1c491", "difficulty": "medium", "final_answer": {"answer": 0.0001, "unit": "mg"}, "id": "half_life_001392_631_14_320", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 631 mg. Its half-life is 14 hours. How many mg remain after 320 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=631 mg, t=320 h, and T_half=14 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 320.0, "half_life": 14.0, "initial_amount": 631.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.64 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 336.2364, \"unit\": \"g\"}", "dedupe_signature": "3685eda19095e283ca43814203e35b9297bd0250a425a1e04d6fc0a0e27b915e", "difficulty": "medium", "final_answer": {"answer": 336.2364, "unit": "g"}, "id": "stoich_mass_001393_carbon_dioxide_7.64", "license": "Apache-2.0", "prompt": "A sample contains 7.64 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 = 7.64 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.64}, "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=0.32 and add it to the current value.\nFinal: {\"answer\": [1.35, 1.314, 0.646], \"unit\": \"temperature_units\"}", "dedupe_signature": "683437e75a4b52464a7eff3b924d17802ff2f1c51d424a40f8c82f16e7ea320c", "difficulty": "hard", "final_answer": {"answer": [1.35, 1.314, 0.646], "unit": "temperature_units"}, "id": "heat_step_001397_0.32_1.45_1.35_1.25_1.35_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=-0.75; current interior values are [1.35, 1.25, 1.35]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [1.35, 1.25, 1.35], "left": 1.45, "r": 0.32, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_001456(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_001456\"}", "dedupe_signature": "7f83b350d9f0212d53297e468cc4a31c98d7d709dc0f5c7015d68ff3e86846c4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_001456"}, "id": "code_001456_normalize_001456", "license": "Apache-2.0", "prompt": "Write a Python function normalize_001456(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": "test", "task_family": "python_code_generation", "variables": {"function": "normalize_001456"}, "verifier": {"function": "normalize_001456", "tests": ["out = normalize_001456([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_001456([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_001456([1, 1]) == [0.5, 0.5]", "try:\n    normalize_001456([1, -1])\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\": [-0.965, -0.069, -0.785], \"unit\": \"temperature_units\"}", "dedupe_signature": "94ca35a0c88a4cdacbdcd42acab7b0f78ae77e06b73485b470ab4c360a86ac48", "difficulty": "hard", "final_answer": {"answer": [-0.965, -0.069, -0.785], "unit": "temperature_units"}, "id": "heat_step_001487_0.42_-1.5_1.45_-1.35_-1.1_-0.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.5, right=-0.1; current interior values are [1.45, -1.35, -1.1]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [1.45, -1.35, -1.1], "left": -1.5, "r": 0.42, "right": -0.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=314 degrees and keep the unit as newtons.\nFinal: {\"answer\": [331.6994, -343.4848], \"unit\": \"N\"}", "dedupe_signature": "36b490c39e87106900710247a5aaebb0319f7e737966449c6bcf750beb4a06da", "difficulty": "medium", "final_answer": {"answer": [331.6994, -343.4848], "unit": "N"}, "id": "vector_components_001489_477.5_314", "license": "Apache-2.0", "prompt": "A vector has magnitude 477.5 N at 314 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=314 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 314, "magnitude": 477.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_001492(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_001492\"}", "dedupe_signature": "45428c66c8f666109241457067eb9ff8c5a621d6945ba0b07d1f2f7082b8355c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_001492"}, "id": "code_001492_weighted_sum_001492", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_001492(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": "test", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_001492"}, "verifier": {"function": "weighted_sum_001492", "tests": ["assert weighted_sum_001492([2, 3], [4, 5]) == 23", "assert weighted_sum_001492([], []) == 0", "try:\n    weighted_sum_001492([1], [1, 2])\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\": [-5.7, -17.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "11bea51af42363cd1f537aa79313ab8e29b96288aa3775a434b0c7883e2c1ade", "difficulty": "medium", "final_answer": {"answer": [-5.7, -17.0], "unit": "dimensionless"}, "id": "line_two_point_001508_6.5_21.5_-5.7_-17", "license": "Apache-2.0", "prompt": "A line passes through points (6.5, -54.05) and (21.5, -139.55). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 6.5, "x2": 21.5, "y1": -54.050000000000004, "y2": -139.55}, "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 Newton's second law F = m a.\n2. Substitute m = 4.15 kg and a = 8.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 36.3125, \"unit\": \"N\"}", "dedupe_signature": "062b976cde6bd9ebbd4c44dc690a821516b38eea2098bd8a0540339a6b8db294", "difficulty": "easy", "final_answer": {"answer": 36.3125, "unit": "N"}, "id": "force_001512_4.15_8.75", "license": "Apache-2.0", "prompt": "A cart has mass 4.15 kg and measured acceleration 8.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.15 kg and a = 8.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.75, "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 = 22.6^2 and multiply by 0.5 * 11.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3013.484, \"unit\": \"J\"}", "dedupe_signature": "d4fbd9dcd12adc162e67ad58a1894feb3d48ba0f65b0aa77b8fe19b3da55ace6", "difficulty": "easy", "final_answer": {"answer": 3013.484, "unit": "J"}, "id": "ke_001513_11.8_22.6", "license": "Apache-2.0", "prompt": "A body of mass 11.8 kg moves at 22.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 22.6^2 and multiply by 0.5 * 11.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.8, "velocity": 22.6}, "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) = -0.53 y, so each step multiplies y by 1 - h*0.53.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 3.5219, \"unit\": \"state_units\"}", "dedupe_signature": "3d158e3b904560b1fe08fa6aedaddd93fd882fe2c683218aa798c84e2a71d888", "difficulty": "medium", "final_answer": {"answer": 3.5219, "unit": "state_units"}, "id": "euler_decay_001521_35_0.53_0.6_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.53 y with y(0)=35, step size h=0.6, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.53, "step": 0.6, "steps": 6}, "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 45194.0 / 1000.\nFinal: {\"answer\": 45.194, \"unit\": \"kg\"}", "dedupe_signature": "12c3e969f4c6f3ae4fef8b31dcd0623bf34ae1dfdf07e7a83f8636726f1bf3b3", "difficulty": "easy", "final_answer": {"answer": 45.194, "unit": "kg"}, "id": "unit_convert_001524_g_to_kg_45194", "license": "Apache-2.0", "prompt": "Convert 45194 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 45194.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 45194.0}, "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 = 26.45^2 and multiply by 0.5 * 19.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6716.184, \"unit\": \"J\"}", "dedupe_signature": "1c31e5cb31fe71746328c9afda9cafccee97a1c551a1cf8a5b8b458e20b8cbab", "difficulty": "easy", "final_answer": {"answer": 6716.184, "unit": "J"}, "id": "ke_001549_19.2_26.45", "license": "Apache-2.0", "prompt": "A body of mass 19.2 kg moves at 26.45 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 = 26.45^2 and multiply by 0.5 * 19.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.2, "velocity": 26.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=14 degrees through the sine of 2 theta.\n3. Substitute v=59.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 168.2867, \"unit\": \"m\"}", "dedupe_signature": "6fbfeb8e581fbdcb46a4a8dc249b8b63e451fce1d6957b64937308dfc9a8881c", "difficulty": "medium", "final_answer": {"answer": 168.2867, "unit": "m"}, "id": "projectile_range_001550_59.3_14", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59.3 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=59.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 14, "gravity": 9.81, "speed": 59.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_001582(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_001582\"}", "dedupe_signature": "d48e4197a89d1d78623146fc146d75acf0e4c18c1d3f90a5b469b7b5c23faf64", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001582"}, "id": "code_001582_safe_mean_001582", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001582(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001582"}, "verifier": {"function": "safe_mean_001582", "tests": ["assert safe_mean_001582([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001582(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001582([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "2f25cb01b24dc447d72e3e7359498a07386b35975339f4ab935be6f8a5680cf1", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001601_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 63.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=715.5 mg, t=104 h, and T_half=86 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 309.4378, \"unit\": \"mg\"}", "dedupe_signature": "82f41914691624dda0ed9a2de322abd1afebdd232942a925fe1170cfbda774f7", "difficulty": "medium", "final_answer": {"answer": 309.4378, "unit": "mg"}, "id": "half_life_001608_715.5_86_104", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 715.5 mg. Its half-life is 86 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=715.5 mg, t=104 h, and T_half=86 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 104.0, "half_life": 86.0, "initial_amount": 715.5}, "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(-4.4)=8.18 and f(1.4)=9.92.\n3. The interval width is 5.8.\nFinal: {\"answer\": 52.49, \"unit\": \"area_units\"}", "dedupe_signature": "be186b235c6f23b05b737a6eb3e4d664ce50dca648e4100ad6b474f9d4881552", "difficulty": "medium", "final_answer": {"answer": 52.49, "unit": "area_units"}, "id": "trapz_linear_001612_0.3_9.5_-4.4_1.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.3x+9.5 from x=-4.4 to x=1.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.4)=8.18 and f(1.4)=9.92.\nThe interval width is 5.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 9.5, "slope": 0.3, "x0": -4.4, "x1": 1.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0115, \"unit\": \"state_units\"}", "dedupe_signature": "d3197d069eee860708d8111adbad1c67ed81f4638aa50f7a66bc509499314719", "difficulty": "medium", "final_answer": {"answer": 0.0115, "unit": "state_units"}, "id": "euler_decay_001647_8_0.83_0.8_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.83 y with y(0)=8, step size h=0.8, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 8.0, "rate": 0.83, "step": 0.8, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [-0.71, -0.547, -0.266], \"unit\": \"temperature_units\"}", "dedupe_signature": "416c8fc2082b8947f09af882a978dfad4703ff39fef44de44e49d14bc59d94e5", "difficulty": "hard", "final_answer": {"answer": [-0.71, -0.547, -0.266], "unit": "temperature_units"}, "id": "heat_step_001667_0.38_-1.35_-1.85_0.65_0.0_-1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.35, right=-1.35; current interior values are [-1.85, 0.65, 0.0]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.85, 0.65, 0.0], "left": -1.35, "r": 0.38, "right": -1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e6986ec853ffc4e465564f0e77a29cf0b41f67c3c6cad3ee8924894e6a97fbe1", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001671_consistent_5ca82cb9_27978", "license": "Apache-2.0", "prompt": "In simulation spec case 27978, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_001672(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_001672\"}", "dedupe_signature": "9fa61f40b7dd9fc68ed61c5ed989e874a09affdf88ddf21e7d7bc59dfe735a0b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001672"}, "id": "code_001672_unit_vector_001672", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001672(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": "test", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001672"}, "verifier": {"function": "unit_vector_001672", "tests": ["ux, uy = unit_vector_001672(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001672(0, 5) == (0, 1)", "try:\n    unit_vector_001672(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "36db1f054056cde240a9003b366f7d3127d8bb85ba845a98c56b6ac58edfb778", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001673_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 63.1 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.2 kg and a = 5.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 22.47, \"unit\": \"N\"}", "dedupe_signature": "f1349a0735ac5396cd66f908a43cf6b41e80833fc25f513c46738e8932fbf05a", "difficulty": "easy", "final_answer": {"answer": 22.47, "unit": "N"}, "id": "force_001674_4.2_5.35", "license": "Apache-2.0", "prompt": "A cart has mass 4.2 kg and measured acceleration 5.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.2 kg and a = 5.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.35, "mass": 4.2}, "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 weighted_sum_001690(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_001690\"}", "dedupe_signature": "fbf66a9df59490b2556b9470ae7bd8986747cd204c6bfa46f2739a3f2041023b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_001690"}, "id": "code_001690_weighted_sum_001690", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_001690(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": "test", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_001690"}, "verifier": {"function": "weighted_sum_001690", "tests": ["assert weighted_sum_001690([2, 3], [4, 5]) == 23", "assert weighted_sum_001690([], []) == 0", "try:\n    weighted_sum_001690([1], [1, 2])\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 = 3.72 * 8.314 * 443 / 28.9.\nFinal: {\"answer\": 474.0879, \"unit\": \"kPa\"}", "dedupe_signature": "0d3bb1b50cf6cf3f3d1a9f2bac09b1030de8c801106fab78047da44c07cbdd8d", "difficulty": "medium", "final_answer": {"answer": 474.0879, "unit": "kPa"}, "id": "ideal_gas_001695_3.72_443_28.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.72 mol, T=443 K, and V=28.9 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 = 3.72 * 8.314 * 443 / 28.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.72, "temp_k": 443, "volume_l": 28.9}, "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 3795 mL to 3.795 L.\n3. Compute M = 0.72 / 3.795.\nFinal: {\"answer\": 0.1897, \"unit\": \"mol/L\"}", "dedupe_signature": "f7c7489fa275c46afa87d4befa22344870de27ab7ea1d06e04943fece0079d21", "difficulty": "medium", "final_answer": {"answer": 0.1897, "unit": "mol/L"}, "id": "molarity_001700_0.72_3795", "license": "Apache-2.0", "prompt": "A solution contains 0.72 mol of solute in 3795 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3795 mL to 3.795 L.\nCompute M = 0.72 / 3.795.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 0.72, "volume_ml": 3795}, "verifier": {"formula": "moles / (volume_ml / 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\": [-1.3, 23.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "eba2dc928dccee46f2d04e62c8395770b7a99515a581017f97c2c8af89451234", "difficulty": "medium", "final_answer": {"answer": [-1.3, 23.0], "unit": "dimensionless"}, "id": "line_two_point_001706_8_20.25_-1.3_23", "license": "Apache-2.0", "prompt": "A line passes through points (8, 12.6) and (20.25, -3.325). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 8.0, "x2": 20.25, "y1": 12.6, "y2": -3.3249999999999993}, "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 x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=32 degrees and keep the unit as newtons.\nFinal: {\"answer\": [76.7484, 47.9577], \"unit\": \"N\"}", "dedupe_signature": "c596effae9e539352a706d3155d9d3742202cb046aa5e5bcf25d6180b4b8aa34", "difficulty": "medium", "final_answer": {"answer": [76.7484, 47.9577], "unit": "N"}, "id": "vector_components_001723_90.5_32", "license": "Apache-2.0", "prompt": "A vector has magnitude 90.5 N at 32 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=32 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 32, "magnitude": 90.5}, "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. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=182.8 V and R=18.1 ohm.\nFinal: {\"answer\": 1846.179, \"unit\": \"W\"}", "dedupe_signature": "ab4f6aedd40610d5f99925930c184f65a6f7d1947ad7d9189d8855075916c8e6", "difficulty": "easy", "final_answer": {"answer": 1846.179, "unit": "W"}, "id": "ohm_power_001733_182.8_18.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 18.1 ohm and voltage 182.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=182.8 V and R=18.1 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 18.1, "voltage": 182.8}, "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\ndef safe_mean_001762(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_001762\"}", "dedupe_signature": "0084cc1480c2e812359151897b963af7ac2bd71e18d0ed03b131e346a8b9d232", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001762"}, "id": "code_001762_safe_mean_001762", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001762(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001762"}, "verifier": {"function": "safe_mean_001762", "tests": ["assert safe_mean_001762([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001762(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001762([])\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=92 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-14.3437, 410.7496], \"unit\": \"N\"}", "dedupe_signature": "1a0ee5999775cbd17cad4767e16b4c5284a8ec8eb3301b27967117361a44fcd2", "difficulty": "medium", "final_answer": {"answer": [-14.3437, 410.7496], "unit": "N"}, "id": "vector_components_001777_411_92", "license": "Apache-2.0", "prompt": "A vector has magnitude 411 N at 92 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=92 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 92, "magnitude": 411.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "7e1875bd004b4b646959afa139888fc02efdb4cc93e08bfa3e2b25946340ffe0", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001779_inconsistent_56040f5d_883651", "license": "Apache-2.0", "prompt": "In instrument manual case 883651, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: 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": "6ec59442b045e0e32e1629f795b466c5ce4684a0db8a1dab39b4149871dc03a1", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001781_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 40 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": "test", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 595 * 0.73 * 18.\nFinal: {\"answer\": 7818.3, \"unit\": \"J\"}", "dedupe_signature": "8a2a3eb08d09f60c310c525fc8c1a754dc70a87d382806850391bfacc9fcdcfd", "difficulty": "easy", "final_answer": {"answer": 7818.3, "unit": "J"}, "id": "heat_q_001786_595_0.73_18", "license": "Apache-2.0", "prompt": "A 595 g sample has specific heat 0.73 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 = 595 * 0.73 * 18.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 18, "heat_capacity": 0.73, "mass_g": 595}, "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(-4.5)=31.75 and f(-3.2)=27.2.\n3. The interval width is 1.3.\nFinal: {\"answer\": 38.3175, \"unit\": \"area_units\"}", "dedupe_signature": "dc87ed451b4ec2926c1818fbfefb8bcda5db7fe07f4f24d4b21b0a885b02d263", "difficulty": "medium", "final_answer": {"answer": 38.3175, "unit": "area_units"}, "id": "trapz_linear_001792_-3.5_16_-4.5_-3.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+16 from x=-4.5 to x=-3.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.5)=31.75 and f(-3.2)=27.2.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 16.0, "slope": -3.5, "x0": -4.5, "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. The function contract has a 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_001798(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_001798\"}", "dedupe_signature": "50995aef92a4789c611e6cc215e133632c6d8952e15b4f39f725ad43f0e3cb80", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_001798"}, "id": "code_001798_weighted_sum_001798", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_001798(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": "test", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_001798"}, "verifier": {"function": "weighted_sum_001798", "tests": ["assert weighted_sum_001798([2, 3], [4, 5]) == 23", "assert weighted_sum_001798([], []) == 0", "try:\n    weighted_sum_001798([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.05^2 and multiply by 0.5 * 23.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2706.7049, \"unit\": \"J\"}", "dedupe_signature": "12ec84d4541afb60d5f795dada3459fb59c354468b65c4d3fb9c72da81c5c9c8", "difficulty": "easy", "final_answer": {"answer": 2706.7049, "unit": "J"}, "id": "ke_001819_23.9_15.05", "license": "Apache-2.0", "prompt": "A body of mass 23.9 kg moves at 15.05 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 = 15.05^2 and multiply by 0.5 * 23.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.9, "velocity": 15.05}, "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) = -0.16 y, so each step multiplies y by 1 - h*0.16.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 19.2908, \"unit\": \"state_units\"}", "dedupe_signature": "d5dd47b40e3e30550019277ba3b58d79218093ba24f424f393b853b59102dbfe", "difficulty": "medium", "final_answer": {"answer": 19.2908, "unit": "state_units"}, "id": "euler_decay_001827_28.5_0.16_0.2_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.16 y with y(0)=28.5, step size h=0.2, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 28.5, "rate": 0.16, "step": 0.2, "steps": 12}, "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 618.0 / 100.\nFinal: {\"answer\": 6.18, \"unit\": \"m\"}", "dedupe_signature": "8ec6f5aa29c087af39fdb2b147a0e966565cc51995251e498243164de32fa06c", "difficulty": "easy", "final_answer": {"answer": 6.18, "unit": "m"}, "id": "unit_convert_001848_cm_to_m_618", "license": "Apache-2.0", "prompt": "Convert 618 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 618.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 618.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.59 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 290.0259, \"unit\": \"g\"}", "dedupe_signature": "81604dfd9d8e4970fbeeae07c7494e40a09055d8ea3cfc381910b6c978b98c1f", "difficulty": "medium", "final_answer": {"answer": 290.0259, "unit": "g"}, "id": "stoich_mass_001861_carbon_dioxide_6.59", "license": "Apache-2.0", "prompt": "A sample contains 6.59 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.59 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.59}, "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=0.1 and add it to the current value.\nFinal: {\"answer\": [-0.95, 0.515, 0.67], \"unit\": \"temperature_units\"}", "dedupe_signature": "9583e7faad71a0cb07b75bb938dde6b155ac1db850441d9d23ddf53d6d3b166b", "difficulty": "hard", "final_answer": {"answer": [-0.95, 0.515, 0.67], "unit": "temperature_units"}, "id": "heat_step_001865_0.1_2.15_-1.55_0.75_0.7_0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=0.35; current interior values are [-1.55, 0.75, 0.7]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.55, 0.75, 0.7], "left": 2.15, "r": 0.1, "right": 0.35}, "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=0.38 and add it to the current value.\nFinal: {\"answer\": [-0.372, -0.621, 0.675], \"unit\": \"temperature_units\"}", "dedupe_signature": "2f4bd576b1f6e209fec7c36a9d66b6d7c373e9c6ff1e75fece2dcad6779d604f", "difficulty": "hard", "final_answer": {"answer": [-0.372, -0.621, 0.675], "unit": "temperature_units"}, "id": "heat_step_001883_0.38_-0.15_-0.6_-0.45_-0.75_2.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.15, right=2.7; current interior values are [-0.6, -0.45, -0.75]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.6, -0.45, -0.75], "left": -0.15, "r": 0.38, "right": 2.7}, "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 = 11.4^2 and multiply by 0.5 * 9.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 594.567, \"unit\": \"J\"}", "dedupe_signature": "646640dd0a0d90745d0148bb0668081b210aaf12ef9057ad330559be4023e5ed", "difficulty": "easy", "final_answer": {"answer": 594.567, "unit": "J"}, "id": "ke_001891_9.15_11.4", "license": "Apache-2.0", "prompt": "A body of mass 9.15 kg moves at 11.4 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 = 11.4^2 and multiply by 0.5 * 9.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.15, "velocity": 11.4}, "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 3970 mL to 3.97 L.\n3. Compute M = 1.375 / 3.97.\nFinal: {\"answer\": 0.3463, \"unit\": \"mol/L\"}", "dedupe_signature": "ef2a6f4c4aaf55a1c73445664e283a337aba162f21f7f36426ac0099119d4ae6", "difficulty": "medium", "final_answer": {"answer": 0.3463, "unit": "mol/L"}, "id": "molarity_001898_1.375_3970", "license": "Apache-2.0", "prompt": "A solution contains 1.375 mol of solute in 3970 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3970 mL to 3.97 L.\nCompute M = 1.375 / 3.97.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.375, "volume_ml": 3970}, "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 safe_mean_001906(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_001906\"}", "dedupe_signature": "6ffa37c534b2d7f5c5a1b1a6eb41aec3bab08bcd5504722ab336ee0a77553d31", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001906"}, "id": "code_001906_safe_mean_001906", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001906(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001906"}, "verifier": {"function": "safe_mean_001906", "tests": ["assert safe_mean_001906([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001906(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001906([])\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 = 1600 * 1.515 * 107.\nFinal: {\"answer\": 259368.0, \"unit\": \"J\"}", "dedupe_signature": "9ce4433692f2ea7b541312f4a36d6285a414914132e19e84616c11813da88c73", "difficulty": "easy", "final_answer": {"answer": 259368.0, "unit": "J"}, "id": "heat_q_001912_1600_1.515_107", "license": "Apache-2.0", "prompt": "A 1600 g sample has specific heat 1.515 J/(g*K). How much heat is needed to raise its temperature by 107 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1600 * 1.515 * 107.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 107, "heat_capacity": 1.515, "mass_g": 1600}, "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 3225 mL to 3.225 L.\n3. Compute M = 2.075 / 3.225.\nFinal: {\"answer\": 0.6434, \"unit\": \"mol/L\"}", "dedupe_signature": "e1d6516ed008c50b1e9039a38b734d56c7a631e983f08e0884b2e22261d6aa94", "difficulty": "medium", "final_answer": {"answer": 0.6434, "unit": "mol/L"}, "id": "molarity_001934_2.075_3225", "license": "Apache-2.0", "prompt": "A solution contains 2.075 mol of solute in 3225 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3225 mL to 3.225 L.\nCompute M = 2.075 / 3.225.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.075, "volume_ml": 3225}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "6eb29973dccd00c3f5db0f52da1886d41c7f43b2b736d8ae32611615e963352d", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_001935_11_0.73_1.3_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.73 y with y(0)=11, step size h=1.3, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 11.0, "rate": 0.73, "step": 1.3, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.8)=20.7 and f(15.3)=58.2.\n3. The interval width is 7.5.\nFinal: {\"answer\": 295.875, \"unit\": \"area_units\"}", "dedupe_signature": "103970d39f0934ec0c621bd7a49999aae37b2236b7f38eb81afb32c5ffe6c792", "difficulty": "medium", "final_answer": {"answer": 295.875, "unit": "area_units"}, "id": "trapz_linear_001936_5_-18.3_7.8_15.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+-18.3 from x=7.8 to x=15.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.8)=20.7 and f(15.3)=58.2.\nThe interval width is 7.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -18.3, "slope": 5.0, "x0": 7.8, "x1": 15.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4189.0 / 1000.\nFinal: {\"answer\": 4.189, \"unit\": \"kg\"}", "dedupe_signature": "f977270552a8b831200b465c298bfafdbd6b5bfbeab04fc1d78ebdfce860beda", "difficulty": "easy", "final_answer": {"answer": 4.189, "unit": "kg"}, "id": "unit_convert_001938_g_to_kg_4189", "license": "Apache-2.0", "prompt": "Convert 4189 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 4189.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 4189.0}, "verifier": {"formula": "value / 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 = 3.56 * 8.314 * 563 / 114.7.\nFinal: {\"answer\": 145.2797, \"unit\": \"kPa\"}", "dedupe_signature": "426882aaeb6c028efd4ae209cf122b1382a875204d0cd98210ce3bf63b3325b2", "difficulty": "medium", "final_answer": {"answer": 145.2797, "unit": "kPa"}, "id": "ideal_gas_001947_3.56_563_114.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.56 mol, T=563 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 = 3.56 * 8.314 * 563 / 114.7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.56, "temp_k": 563, "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. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 111.0 + 273.15.\nFinal: {\"answer\": 384.15, \"unit\": \"K\"}", "dedupe_signature": "95e8ebb078ddb6abdd4d9c265074148bb8ae14d1355add24c3709a39f5caa127", "difficulty": "easy", "final_answer": {"answer": 384.15, "unit": "K"}, "id": "unit_convert_001956_c_to_k_111", "license": "Apache-2.0", "prompt": "Convert 111 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 111.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 111.0}, "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. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c4b60a96286ef44d0aa6a06c1da622766e96844822c8c6bcce24d9f66064492c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001959_inconsistent_7481c798_826578", "license": "Apache-2.0", "prompt": "In instrument manual case 826578, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.95 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 217.8495, \"unit\": \"g\"}", "dedupe_signature": "bab6bac40dfedd05cc50f0277805af1a0bc91891a665b0d12d030d6b9ca39cd1", "difficulty": "medium", "final_answer": {"answer": 217.8495, "unit": "g"}, "id": "stoich_mass_001987_carbon_dioxide_4.95", "license": "Apache-2.0", "prompt": "A sample contains 4.95 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.95 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.95}, "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\nimport math\n\ndef unit_vector_001996(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_001996\"}", "dedupe_signature": "2d520fc50491f897e80e6e8f57ef075cc5c300af69e6177bc36397ace284cfaf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001996"}, "id": "code_001996_unit_vector_001996", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001996(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": "test", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001996"}, "verifier": {"function": "unit_vector_001996", "tests": ["ux, uy = unit_vector_001996(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001996(0, 5) == (0, 1)", "try:\n    unit_vector_001996(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.4^2 and multiply by 0.5 * 16.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16460.856, \"unit\": \"J\"}", "dedupe_signature": "30aaabc737fd5f78865f63a1f992de5a47724e092ca2679cc384872fc8b40d0d", "difficulty": "easy", "final_answer": {"answer": 16460.856, "unit": "J"}, "id": "ke_001999_16.7_44.4", "license": "Apache-2.0", "prompt": "A body of mass 16.7 kg moves at 44.4 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 = 44.4^2 and multiply by 0.5 * 16.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.7, "velocity": 44.4}, "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) = -0.71 y, so each step multiplies y by 1 - h*0.71.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "acf42bc3bd7de8e3cce0f794cf6975959811afe2e3f99e16ecb51222dafe1c7b", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002025_55.5_0.71_1.45_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.71 y with y(0)=55.5, step size h=1.45, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 55.5, "rate": 0.71, "step": 1.45, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.9)=28.83 and f(3.6)=-2.62.\n3. The interval width is 8.5.\nFinal: {\"answer\": 111.3925, \"unit\": \"area_units\"}", "dedupe_signature": "1947ff793425a6398326012dd0589cb70a1a257cb7c296bb9458ec61d197fde1", "difficulty": "medium", "final_answer": {"answer": 111.3925, "unit": "area_units"}, "id": "trapz_linear_002026_-3.7_10.7_-4.9_3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.7x+10.7 from x=-4.9 to x=3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.9)=28.83 and f(3.6)=-2.62.\nThe interval width is 8.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 10.7, "slope": -3.7, "x0": -4.9, "x1": 3.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.9, -8.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "ff0221038cd36b2ffa4cfdc0ae294d630fad52433a9aa7f4a74a398dec0fe82d", "difficulty": "medium", "final_answer": {"answer": [0.9, -8.75], "unit": "dimensionless"}, "id": "line_two_point_002030_-13.5_-6.75_0.9_-8.75", "license": "Apache-2.0", "prompt": "A line passes through points (-13.5, -20.9) and (-6.75, -14.825). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -13.5, "x2": -6.75, "y1": -20.9, "y2": -14.825}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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=17.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 25.8139, \"unit\": \"m\"}", "dedupe_signature": "5b5fa5429da8c0543c6985341ec666920008b3a0d2c9f6be9e1525a0cd4a63f7", "difficulty": "medium", "final_answer": {"answer": 25.8139, "unit": "m"}, "id": "projectile_range_002036_17.1_60", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 17.1 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=17.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 60, "gravity": 9.81, "speed": 17.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_002050(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_002050\"}", "dedupe_signature": "86252e0e4a50fb536210d2e7c46c03120f068ec374a8ba131b1dd95b620086d3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_002050"}, "id": "code_002050_clamp_002050", "license": "Apache-2.0", "prompt": "Write a Python function clamp_002050(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": "test", "task_family": "python_code_generation", "variables": {"function": "clamp_002050"}, "verifier": {"function": "clamp_002050", "tests": ["assert clamp_002050(5, 0, 10) == 5", "assert clamp_002050(-2, 0, 10) == 0", "assert clamp_002050(12, 0, 10) == 10", "try:\n    clamp_002050(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=81 degrees through the sine of 2 theta.\n3. Substitute v=65.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 134.3197, \"unit\": \"m\"}", "dedupe_signature": "481310f4b26d1a150d3c7cf099e94dbb7871a8bfe949cb9c45ffa3162de9faf9", "difficulty": "medium", "final_answer": {"answer": 134.3197, "unit": "m"}, "id": "projectile_range_002072_65.3_81", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 65.3 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=65.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 81, "gravity": 9.81, "speed": 65.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.62 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 362.3149, \"unit\": \"g\"}", "dedupe_signature": "f7b954bc39f651e54301ef8e0c0dcd53c8f45448edf744f0f440184b83709aa0", "difficulty": "medium", "final_answer": {"answer": 362.3149, "unit": "g"}, "id": "stoich_mass_002095_calcium_carbonate_3.62", "license": "Apache-2.0", "prompt": "A sample contains 3.62 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.62 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.62}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.6)=39.54 and f(3)=-12.3.\n3. The interval width is 9.6.\nFinal: {\"answer\": 130.752, \"unit\": \"area_units\"}", "dedupe_signature": "be32efcdac30c9e6d5358e3e2ed33f1ebe9cc3c9c9a336656a1af2644a2e4af3", "difficulty": "medium", "final_answer": {"answer": 130.752, "unit": "area_units"}, "id": "trapz_linear_002098_-5.4_3.9_-6.6_3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.4x+3.9 from x=-6.6 to x=3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.6)=39.54 and f(3)=-12.3.\nThe interval width is 9.6.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 3.9, "slope": -5.4, "x0": -6.6, "x1": 3.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22645.0 / 1000.\nFinal: {\"answer\": 22.645, \"unit\": \"kg\"}", "dedupe_signature": "2c8b361d0ad3cfb6373310f1c3f7785e7d723380ddada1544082db6ab49eb934", "difficulty": "easy", "final_answer": {"answer": 22.645, "unit": "kg"}, "id": "unit_convert_002100_g_to_kg_22645", "license": "Apache-2.0", "prompt": "Convert 22645 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 22645.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 22645.0}, "verifier": {"formula": "value / 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=658 mg, t=210.5 h, and T_half=41 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 18.7367, \"unit\": \"mg\"}", "dedupe_signature": "f31072c263dea67b80cace7ce776274d9adca4ca9dccb4fa9e6e19716c975d5f", "difficulty": "medium", "final_answer": {"answer": 18.7367, "unit": "mg"}, "id": "half_life_002112_658_41_210.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 658 mg. Its half-life is 41 hours. How many mg remain after 210.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=658 mg, t=210.5 h, and T_half=41 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 210.5, "half_life": 41.0, "initial_amount": 658.0}, "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 1620 mL to 1.62 L.\n3. Compute M = 4.455 / 1.62.\nFinal: {\"answer\": 2.75, \"unit\": \"mol/L\"}", "dedupe_signature": "0f2b4e21b2ef1dff9a03c93d4eeb18db5b305bb165be0fb95e0f78966a0eafd9", "difficulty": "medium", "final_answer": {"answer": 2.75, "unit": "mol/L"}, "id": "molarity_002114_4.455_1620", "license": "Apache-2.0", "prompt": "A solution contains 4.455 mol of solute in 1620 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1620 mL to 1.62 L.\nCompute M = 4.455 / 1.62.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.455, "volume_ml": 1620}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.7, 9.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "7604e773743110665f596d013209be2ac05b51d494c0b4fa2814d8a7ab4a7bbe", "difficulty": "medium", "final_answer": {"answer": [-6.7, 9.75], "unit": "dimensionless"}, "id": "line_two_point_002120_-2.5_5.5_-6.7_9.75", "license": "Apache-2.0", "prompt": "A line passes through points (-2.5, 26.5) and (5.5, -27.1). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -2.5, "x2": 5.5, "y1": 26.5, "y2": -27.1}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: 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": "1e22c5cfd2d0dce99d4490a20950d9995db912f755f1ccc90c2d136bb514538b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_002141_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 [-1.45, 2.25, 0.95], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "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=32 degrees through the sine of 2 theta.\n3. Substitute v=51.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 242.9996, \"unit\": \"m\"}", "dedupe_signature": "cfb78545b4efe4f0222fe7cfb61d0446ce2afd178928fbb8af39c563cc60ddb9", "difficulty": "medium", "final_answer": {"answer": 242.9996, "unit": "m"}, "id": "projectile_range_002144_51.5_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 51.5 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=51.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "gravity": 9.81, "speed": 51.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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\": 37.2244, \"unit\": \"state_units\"}", "dedupe_signature": "f27ec0495e2916b0c89a9703570059020f2c9ce8777126bfda3bffb0617242ca", "difficulty": "medium", "final_answer": {"answer": 37.2244, "unit": "state_units"}, "id": "euler_decay_002151_75.5_0.15_1.4_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=75.5, 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) = -0.15 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": "test", "task_family": "numerical_ode", "variables": {"initial_y": 75.5, "rate": 0.15, "step": 1.4, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.6)=11.08 and f(2.5)=-23.\n3. The interval width is 7.1.\nFinal: {\"answer\": -42.316, \"unit\": \"area_units\"}", "dedupe_signature": "ba1f126ac5d978f8a0b0fc6c44be2153b75374bbee165ae490dd6d364601d2bc", "difficulty": "medium", "final_answer": {"answer": -42.316, "unit": "area_units"}, "id": "trapz_linear_002170_-4.8_-11_-4.6_2.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.8x+-11 from x=-4.6 to x=2.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.6)=11.08 and f(2.5)=-23.\nThe interval width is 7.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -11.0, "slope": -4.8, "x0": -4.6, "x1": 2.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 33.55^2 and multiply by 0.5 * 26.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 15054.9334, \"unit\": \"J\"}", "dedupe_signature": "81b41d2bd1eea3a4918730e3f0d1afeac26eab1f1e151ddf768970f1adc51295", "difficulty": "easy", "final_answer": {"answer": 15054.9334, "unit": "J"}, "id": "ke_002179_26.75_33.55", "license": "Apache-2.0", "prompt": "A body of mass 26.75 kg moves at 33.55 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 = 33.55^2 and multiply by 0.5 * 26.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.75, "velocity": 33.55}, "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 300 mL to 0.3 L.\n3. Compute M = 2.155 / 0.3.\nFinal: {\"answer\": 7.1833, \"unit\": \"mol/L\"}", "dedupe_signature": "4b3fe25a1248cd10761563d76c90b323981a9a777b15945e3130cc2926f11455", "difficulty": "medium", "final_answer": {"answer": 7.1833, "unit": "mol/L"}, "id": "molarity_002186_2.155_300", "license": "Apache-2.0", "prompt": "A solution contains 2.155 mol of solute in 300 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 300 mL to 0.3 L.\nCompute M = 2.155 / 0.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.155, "volume_ml": 300}, "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=138 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-124.8483, 112.4139], \"unit\": \"N\"}", "dedupe_signature": "c0311e9a2375180065081eb5512c88a3db615fba1d1c54872a8c51d1d8252cd0", "difficulty": "medium", "final_answer": {"answer": [-124.8483, 112.4139], "unit": "N"}, "id": "vector_components_002191_168_138", "license": "Apache-2.0", "prompt": "A vector has magnitude 168 N at 138 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=138 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 138, "magnitude": 168.0}, "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": "3b0c4579cbbae9cd42ad6cf06dd1bddb4a884feb7c1f0bc8649c4afac537133a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002193_consistent_03f5e041_512665", "license": "Apache-2.0", "prompt": "In model card equation case 512665, 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": "test", "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: 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": "ef0f9452a7d8ff2722fae51428f979d73a78084ef83ba3938534868eee23729a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_002195_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse sensor records in release 741417, 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": "test", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 39.85^2 and multiply by 0.5 * 14.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11394.0614, \"unit\": \"J\"}", "dedupe_signature": "3e9fb2445c73762da6070b7c218a96474a2e050f3fb8581d0f218a9f4de98853", "difficulty": "easy", "final_answer": {"answer": 11394.0614, "unit": "J"}, "id": "ke_002197_14.35_39.85", "license": "Apache-2.0", "prompt": "A body of mass 14.35 kg moves at 39.85 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 = 39.85^2 and multiply by 0.5 * 14.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.35, "velocity": 39.85}, "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 = 1395 * 4.105 * 48.\nFinal: {\"answer\": 274870.8, \"unit\": \"J\"}", "dedupe_signature": "cc20003559ad60856d83f5321e00e0c70d7ca5a29e89953fffe6b47fcd32a735", "difficulty": "easy", "final_answer": {"answer": 274870.8, "unit": "J"}, "id": "heat_q_002200_1395_4.105_48", "license": "Apache-2.0", "prompt": "A 1395 g sample has specific heat 4.105 J/(g*K). How much heat is needed to raise its temperature by 48 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1395 * 4.105 * 48.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 48, "heat_capacity": 4.105, "mass_g": 1395}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=34.4 V and R=167.8 ohm.\nFinal: {\"answer\": 7.0522, \"unit\": \"W\"}", "dedupe_signature": "6e7bdf199f68128af5171cb9e4a0fef3e91e824a7cf41fa896562158b4e042ba", "difficulty": "easy", "final_answer": {"answer": 7.0522, "unit": "W"}, "id": "ohm_power_002201_34.4_167.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 167.8 ohm and voltage 34.4 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=34.4 V and R=167.8 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 167.8, "voltage": 34.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.4)=-14.68 and f(4.1)=-8.03.\n3. The interval width is 9.5.\nFinal: {\"answer\": -107.8725, \"unit\": \"area_units\"}", "dedupe_signature": "76b7631af7ea6b425ca1fd020239be348cccc133834d5d2a0674b8ec95307a02", "difficulty": "medium", "final_answer": {"answer": -107.8725, "unit": "area_units"}, "id": "trapz_linear_002224_0.7_-10.9_-5.4_4.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+-10.9 from x=-5.4 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(-5.4)=-14.68 and f(4.1)=-8.03.\nThe interval width is 9.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -10.9, "slope": 0.7, "x0": -5.4, "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. 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": "304c1fe6c5b30c487e46905cba0e49599ae10870718b20f9bab584bee65655c5", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002229_consistent_4153435f_340013", "license": "Apache-2.0", "prompt": "In student derivation case 340013, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "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 = 5.64 * 8.314 * 584 / 33.3.\nFinal: {\"answer\": 822.352, \"unit\": \"kPa\"}", "dedupe_signature": "dd6d4ebef1125d5ce38cd2c2f4627fbc14cc49c80356fdcff74f2bbc27844c5c", "difficulty": "medium", "final_answer": {"answer": 822.352, "unit": "kPa"}, "id": "ideal_gas_002235_5.64_584_33.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.64 mol, T=584 K, and V=33.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.64 * 8.314 * 584 / 33.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 5.64, "temp_k": 584, "volume_l": 33.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 204.5 / 100.\nFinal: {\"answer\": 2.045, \"unit\": \"m\"}", "dedupe_signature": "8f983997270e2fb0b68e10a0cdc7706f81cc775115a420e1c1cfc48a09e4e409", "difficulty": "easy", "final_answer": {"answer": 2.045, "unit": "m"}, "id": "unit_convert_002244_cm_to_m_204.5", "license": "Apache-2.0", "prompt": "Convert 204.5 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 204.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 204.5}, "verifier": {"formula": "value / 100", "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": "5f0e28c0cc9fe36376c105835ea368bac7b2a8b3bd0dbb6443acb3dbb60ff59b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_002267_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory sensor record from batch 28941 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": "test", "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4685 mL to 4.685 L.\n3. Compute M = 1.57 / 4.685.\nFinal: {\"answer\": 0.3351, \"unit\": \"mol/L\"}", "dedupe_signature": "0ad3720887f50b110a25fd4dd5fff406f282b657b8270171c8c4dd19d5b7122c", "difficulty": "medium", "final_answer": {"answer": 0.3351, "unit": "mol/L"}, "id": "molarity_002276_1.57_4685", "license": "Apache-2.0", "prompt": "A solution contains 1.57 mol of solute in 4685 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4685 mL to 4.685 L.\nCompute M = 1.57 / 4.685.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.57, "volume_ml": 4685}, "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 = 2.3 * 8.314 * 513 / 72.7.\nFinal: {\"answer\": 134.9338, \"unit\": \"kPa\"}", "dedupe_signature": "e4d5ca64faef084e0e2e5a0be8d39b03c5633abd080f6bafcb8950474a4bc80d", "difficulty": "medium", "final_answer": {"answer": 134.9338, "unit": "kPa"}, "id": "ideal_gas_002289_2.3_513_72.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.3 mol, T=513 K, and V=72.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.3 * 8.314 * 513 / 72.7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.3, "temp_k": 513, "volume_l": 72.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1870 * 4.005 * 7.\nFinal: {\"answer\": 52425.45, \"unit\": \"J\"}", "dedupe_signature": "a6fe3c1866028d20ea68f82e7af55e3f00581d02e0232e84ed3f295dd86791d3", "difficulty": "easy", "final_answer": {"answer": 52425.45, "unit": "J"}, "id": "heat_q_002308_1870_4.005_7", "license": "Apache-2.0", "prompt": "A 1870 g sample has specific heat 4.005 J/(g*K). How much heat is needed to raise its temperature by 7 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1870 * 4.005 * 7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 7, "heat_capacity": 4.005, "mass_g": 1870}, "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 4055 mL to 4.055 L.\n3. Compute M = 2.24 / 4.055.\nFinal: {\"answer\": 0.5524, \"unit\": \"mol/L\"}", "dedupe_signature": "119963ba37a5c75181963f2a3a14bb5d8018c78e6c6c615c4d3996ecf95d5673", "difficulty": "medium", "final_answer": {"answer": 0.5524, "unit": "mol/L"}, "id": "molarity_002312_2.24_4055", "license": "Apache-2.0", "prompt": "A solution contains 2.24 mol of solute in 4055 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4055 mL to 4.055 L.\nCompute M = 2.24 / 4.055.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.24, "volume_ml": 4055}, "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 828.0 / 100.\nFinal: {\"answer\": 8.28, \"unit\": \"m\"}", "dedupe_signature": "bea152992e62ffae4b6a25383c7e33cd37c770dbff1f5dc6ec59e8ee8eb02e02", "difficulty": "easy", "final_answer": {"answer": 8.28, "unit": "m"}, "id": "unit_convert_002316_cm_to_m_828", "license": "Apache-2.0", "prompt": "Convert 828 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 828.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 828.0}, "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=690 mg, t=201 h, and T_half=120 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 216.0846, \"unit\": \"mg\"}", "dedupe_signature": "0acbc58c52c5cd0679829a5fee07889587e1b408ee811bad16cb49973ae81ba0", "difficulty": "medium", "final_answer": {"answer": 216.0846, "unit": "mg"}, "id": "half_life_002328_690_120_201", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 690 mg. Its half-life is 120 hours. How many mg remain after 201 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=690 mg, t=201 h, and T_half=120 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 201.0, "half_life": 120.0, "initial_amount": 690.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.8)=-48.62 and f(-1.8)=-27.02.\n3. The interval width is 4.\nFinal: {\"answer\": -151.28, \"unit\": \"area_units\"}", "dedupe_signature": "7a1cf7717b00235e68dbec81593ea0a65c52e57e30ef19615aa151b0a5171e6c", "difficulty": "medium", "final_answer": {"answer": -151.28, "unit": "area_units"}, "id": "trapz_linear_002332_5.4_-17.3_-5.8_-1.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.4x+-17.3 from x=-5.8 to x=-1.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.8)=-48.62 and f(-1.8)=-27.02.\nThe interval width is 4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -17.3, "slope": 5.4, "x0": -5.8, "x1": -1.7999999999999998}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.95 kg and a = 12.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 100.5675, \"unit\": \"N\"}", "dedupe_signature": "8f706309a1ab9fdc965aa123b13fdc33252e72975bb0e48e6809ae2a778e87a4", "difficulty": "easy", "final_answer": {"answer": 100.5675, "unit": "N"}, "id": "force_002358_7.95_12.65", "license": "Apache-2.0", "prompt": "A cart has mass 7.95 kg and measured acceleration 12.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.95 kg and a = 12.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.65, "mass": 7.95}, "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) = -0.8 y, so each step multiplies y by 1 - h*0.8.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0024, \"unit\": \"state_units\"}", "dedupe_signature": "d9787d877bbef01e2820a092eb037eaec4663483b9f8db931bf579b2afada997", "difficulty": "medium", "final_answer": {"answer": 0.0024, "unit": "state_units"}, "id": "euler_decay_002367_38_0.8_1.5_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.8 y with y(0)=38, step size h=1.5, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 38.0, "rate": 0.8, "step": 1.5, "steps": 6}, "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\nimport math\n\ndef unit_vector_002374(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_002374\"}", "dedupe_signature": "3d6859ad97fc0e53a347490056159e403b7abb8d0e3f880e0e8973ea9808cc6b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002374"}, "id": "code_002374_unit_vector_002374", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002374(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": "test", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002374"}, "verifier": {"function": "unit_vector_002374", "tests": ["ux, uy = unit_vector_002374(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002374(0, 5) == (0, 1)", "try:\n    unit_vector_002374(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=113 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-42.5897, 100.335], \"unit\": \"N\"}", "dedupe_signature": "6ddfa9ac56f36179f0ee93798dfcc5c12797a5f5a1c20b1b1b35621900c25b5d", "difficulty": "medium", "final_answer": {"answer": [-42.5897, 100.335], "unit": "N"}, "id": "vector_components_002389_109_113", "license": "Apache-2.0", "prompt": "A vector has magnitude 109 N at 113 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=113 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 113, "magnitude": 109.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_002392(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_002392\"}", "dedupe_signature": "b9dca32479485e404efaf51e5d9201105af841c853f09a636a2055d1e7fbdc81", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_002392"}, "id": "code_002392_clamp_002392", "license": "Apache-2.0", "prompt": "Write a Python function clamp_002392(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": "test", "task_family": "python_code_generation", "variables": {"function": "clamp_002392"}, "verifier": {"function": "clamp_002392", "tests": ["assert clamp_002392(5, 0, 10) == 5", "assert clamp_002392(-2, 0, 10) == 0", "assert clamp_002392(12, 0, 10) == 10", "try:\n    clamp_002392(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=15 degrees through the sine of 2 theta.\n3. Substitute v=83.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 351.9679, \"unit\": \"m\"}", "dedupe_signature": "059a8f05a7368f9f3f01aeea99b619282f70f03ce8779e83183dcaadc484e013", "difficulty": "medium", "final_answer": {"answer": 351.9679, "unit": "m"}, "id": "projectile_range_002396_83.1_15", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 83.1 m/s and angle 15 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=15 degrees through the sine of 2 theta.\nSubstitute v=83.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 15, "gravity": 9.81, "speed": 83.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=150 mg, t=256 h, and T_half=23 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0669, \"unit\": \"mg\"}", "dedupe_signature": "72b8e6b179667fa27e1b7fadf3953632620a583f668151ee5bad2668b751287d", "difficulty": "medium", "final_answer": {"answer": 0.0669, "unit": "mg"}, "id": "half_life_002400_150_23_256", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 150 mg. Its half-life is 23 hours. How many mg remain after 256 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=150 mg, t=256 h, and T_half=23 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 256.0, "half_life": 23.0, "initial_amount": 150.0}, "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: 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": "5b308799064ffab821fd5f0d0fed5e7a139a1652e2646cb5e1586e3d55cbd2e5", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_002411_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field sensor records in release 45215, 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": "test", "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 the ideal gas law P V = n R 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 * 501 / 65.0.\nFinal: {\"answer\": 51.2654, \"unit\": \"kPa\"}", "dedupe_signature": "4174efe2e10a3cfa928899275570692bdb5e8212e517725dc14a578b90b4482d", "difficulty": "medium", "final_answer": {"answer": 51.2654, "unit": "kPa"}, "id": "ideal_gas_002415_0.8_501_65.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.8 mol, T=501 K, and V=65.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.8 * 8.314 * 501 / 65.0.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 0.8, "temp_k": 501, "volume_l": 65.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-10)=-25.8 and f(-8)=-24.4.\n3. The interval width is 2.\nFinal: {\"answer\": -50.2, \"unit\": \"area_units\"}", "dedupe_signature": "ecc965a88ac2333303168610ccb88a5bfb76814f0e0a4eba2b36b393bde780ca", "difficulty": "medium", "final_answer": {"answer": -50.2, "unit": "area_units"}, "id": "trapz_linear_002422_0.7_-18.8_-10_-8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+-18.8 from x=-10 to x=-8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-10)=-25.8 and f(-8)=-24.4.\nThe interval width is 2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -18.8, "slope": 0.7, "x0": -10.0, "x1": -8.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1410 * 3.31 * 40.\nFinal: {\"answer\": 186684.0, \"unit\": \"J\"}", "dedupe_signature": "d626123d5602230dd820d08e49e81d013943f563c5e64b7640c56d8000a9d8cc", "difficulty": "easy", "final_answer": {"answer": 186684.0, "unit": "J"}, "id": "heat_q_002434_1410_3.31_40", "license": "Apache-2.0", "prompt": "A 1410 g sample has specific heat 3.31 J/(g*K). How much heat is needed to raise its temperature by 40 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1410 * 3.31 * 40.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 40, "heat_capacity": 3.31, "mass_g": 1410}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=96.1 V and R=47.7 ohm.\nFinal: {\"answer\": 193.6103, \"unit\": \"W\"}", "dedupe_signature": "1c6d91df20c7290f73c17774de843d0b9bc0a4e161accba8aae411588a806870", "difficulty": "easy", "final_answer": {"answer": 193.6103, "unit": "W"}, "id": "ohm_power_002435_96.1_47.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 47.7 ohm and voltage 96.1 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=96.1 V and R=47.7 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 47.7, "voltage": 96.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.281, 0.112, 0.928], \"unit\": \"temperature_units\"}", "dedupe_signature": "cc57d402e18eb201c1c1fe64043c31fc852f5d0beba09a6adb7c5d1615afd9a3", "difficulty": "hard", "final_answer": {"answer": [1.281, 0.112, 0.928], "unit": "temperature_units"}, "id": "heat_step_002477_0.22_1.8_2.15_-1.45_2.05_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=1.8, right=0.45; current interior values are [2.15, -1.45, 2.05]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [2.15, -1.45, 2.05], "left": 1.8, "r": 0.22, "right": 0.45}, "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=637.5 mg, t=89.5 h, and T_half=21 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 33.2291, \"unit\": \"mg\"}", "dedupe_signature": "a03c451541b9e0122f378d9b03efce4b26aa69be2276e60c133279743f773bac", "difficulty": "medium", "final_answer": {"answer": 33.2291, "unit": "mg"}, "id": "half_life_002544_637.5_21_89.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 637.5 mg. Its half-life is 21 hours. How many mg remain after 89.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=637.5 mg, t=89.5 h, and T_half=21 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 89.5, "half_life": 21.0, "initial_amount": 637.5}, "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) = -0.29 y, so each step multiplies y by 1 - h*0.29.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 41.6902, \"unit\": \"state_units\"}", "dedupe_signature": "6573ece69f8b364b26919e3c81f1a25349c74271cf88f03a6ee6f7c6b74a53db", "difficulty": "medium", "final_answer": {"answer": 41.6902, "unit": "state_units"}, "id": "euler_decay_002565_60_0.29_0.3_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.29 y with y(0)=60, step size h=0.3, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 60.0, "rate": 0.29, "step": 0.3, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.9)=56.86 and f(14)=79.3.\n3. The interval width is 5.1.\nFinal: {\"answer\": 347.208, \"unit\": \"area_units\"}", "dedupe_signature": "ddfcb83937227f05c3c1d07fbee987567701d5c28fca7bf21a57302aa9ed34da", "difficulty": "medium", "final_answer": {"answer": 347.208, "unit": "area_units"}, "id": "trapz_linear_002566_4.4_17.7_8.9_14", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+17.7 from x=8.9 to x=14. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.9)=56.86 and f(14)=79.3.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 17.7, "slope": 4.4, "x0": 8.9, "x1": 14.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2103.5 / 100.\nFinal: {\"answer\": 21.035, \"unit\": \"m\"}", "dedupe_signature": "9052bceced435476ea1ccc05482685411bd593f994b5aba4ee4e1cbd810a1be8", "difficulty": "easy", "final_answer": {"answer": 21.035, "unit": "m"}, "id": "unit_convert_002586_cm_to_m_2103.5", "license": "Apache-2.0", "prompt": "Convert 2103.5 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 2103.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 2103.5}, "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 = 31.5^2 and multiply by 0.5 * 5.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2579.85, \"unit\": \"J\"}", "dedupe_signature": "6d0a625134dfd40e2ce004b0cc7a7b6d8057ff958f3e3f0eb9ec26c5ce9b3c76", "difficulty": "easy", "final_answer": {"answer": 2579.85, "unit": "J"}, "id": "ke_002593_5.2_31.5", "license": "Apache-2.0", "prompt": "A body of mass 5.2 kg moves at 31.5 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 = 31.5^2 and multiply by 0.5 * 5.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.2, "velocity": 31.5}, "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\": [-0.15, -1.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "bb6c35574f02e78004271f73484fcbf9ba1c00e332f59dd406f917b4c5e98f48", "difficulty": "medium", "final_answer": {"answer": [-0.15, -1.25], "unit": "dimensionless"}, "id": "line_two_point_002606_7_11.5_-0.15_-1.25", "license": "Apache-2.0", "prompt": "A line passes through points (7, -2.3) and (11.5, -2.975). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 7.0, "x2": 11.5, "y1": -2.3, "y2": -2.9749999999999996}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.2 kg and a = 5.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.9, \"unit\": \"N\"}", "dedupe_signature": "021e2d289b2302c3a40be02bf8c039c25f136b0aa173232985bc94c676ac0972", "difficulty": "easy", "final_answer": {"answer": 52.9, "unit": "N"}, "id": "force_002610_9.2_5.75", "license": "Apache-2.0", "prompt": "A cart has mass 9.2 kg and measured acceleration 5.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.2 kg and a = 5.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.75, "mass": 9.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.43 * 8.314 * 451 / 1.8.\nFinal: {\"answer\": 11311.3356, \"unit\": \"kPa\"}", "dedupe_signature": "11f3370852d295cc3e9f009f908aae22bb3f0f25cbd2fa6475e65550d9a3e72e", "difficulty": "medium", "final_answer": {"answer": 11311.3356, "unit": "kPa"}, "id": "ideal_gas_002613_5.43_451_1.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.43 mol, T=451 K, and V=1.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.43 * 8.314 * 451 / 1.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 5.43, "temp_k": 451, "volume_l": 1.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 4.6294, \"unit\": \"state_units\"}", "dedupe_signature": "c9a4c6ec18dad8eb110a811dc2a041f834324600e632a9f6896c0dc2ea2283a7", "difficulty": "medium", "final_answer": {"answer": 4.6294, "unit": "state_units"}, "id": "euler_decay_002619_10.5_0.32_1.05_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.32 y with y(0)=10.5, step size h=1.05, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 10.5, "rate": 0.32, "step": 1.05, "steps": 2}, "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\": [-9.65, 24.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "1bfd4e38080524f80747f5ffe4d47b2d9fc7f358a2580f5ded2debe4e0d7cb9a", "difficulty": "medium", "final_answer": {"answer": [-9.65, 24.5], "unit": "dimensionless"}, "id": "line_two_point_002624_7.5_19_-9.65_24.5", "license": "Apache-2.0", "prompt": "A line passes through points (7.5, -47.875) and (19, -158.85). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 7.5, "x2": 19.0, "y1": -47.875, "y2": -158.85}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.95^2 and multiply by 0.5 * 23.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 741.0493, \"unit\": \"J\"}", "dedupe_signature": "caa1642d3890e4f6a09f49d63f88020ee6f5a26c10915208f434d66e8db12210", "difficulty": "easy", "final_answer": {"answer": 741.0493, "unit": "J"}, "id": "ke_002629_23.45_7.95", "license": "Apache-2.0", "prompt": "A body of mass 23.45 kg moves at 7.95 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 = 7.95^2 and multiply by 0.5 * 23.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.45, "velocity": 7.95}, "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=799.5 mg, t=356.5 h, and T_half=117.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 97.6069, \"unit\": \"mg\"}", "dedupe_signature": "faf9a99fcc7b745fc532ad408d1df5670bd34bdfbf50b5565422551e94833607", "difficulty": "medium", "final_answer": {"answer": 97.6069, "unit": "mg"}, "id": "half_life_002634_799.5_117.5_356.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 799.5 mg. Its half-life is 117.5 hours. How many mg remain after 356.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=799.5 mg, t=356.5 h, and T_half=117.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 356.5, "half_life": 117.5, "initial_amount": 799.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.15^2 and multiply by 0.5 * 7.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1194.1566, \"unit\": \"J\"}", "dedupe_signature": "72c3f472960cb3a2f59ce4fccc809d3b613b4848ae2c5447314b6835e26a2bcc", "difficulty": "easy", "final_answer": {"answer": 1194.1566, "unit": "J"}, "id": "ke_002647_7.25_18.15", "license": "Apache-2.0", "prompt": "A body of mass 7.25 kg moves at 18.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.15^2 and multiply by 0.5 * 7.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.25, "velocity": 18.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.66 * 8.314 * 430 / 91.1.\nFinal: {\"answer\": 25.9003, \"unit\": \"kPa\"}", "dedupe_signature": "9c67ae82333496b69c2c365cf7fc0885c5f6304ef4de51b5498eef06a1c79d9f", "difficulty": "medium", "final_answer": {"answer": 25.9003, "unit": "kPa"}, "id": "ideal_gas_002649_0.66_430_91.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.66 mol, T=430 K, and V=91.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.66 * 8.314 * 430 / 91.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 0.66, "temp_k": 430, "volume_l": 91.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 435.5 / 100.\nFinal: {\"answer\": 4.355, \"unit\": \"m\"}", "dedupe_signature": "8dfc38e7e79e03857b675f1c7a22c9c6af47467ac5742b572843cf963b5fc2ec", "difficulty": "easy", "final_answer": {"answer": 4.355, "unit": "m"}, "id": "unit_convert_002658_cm_to_m_435.5", "license": "Apache-2.0", "prompt": "Convert 435.5 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 435.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 435.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.3 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 189.243, \"unit\": \"g\"}", "dedupe_signature": "3eb73cedda4b4cf91763ac7a6a0167fd9403595cb25bff4c846303c8d07f744c", "difficulty": "medium", "final_answer": {"answer": 189.243, "unit": "g"}, "id": "stoich_mass_002689_carbon_dioxide_4.3", "license": "Apache-2.0", "prompt": "A sample contains 4.3 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.3 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.3}, "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 = 4.31 * 8.314 * 467 / 118.4.\nFinal: {\"answer\": 141.3359, \"unit\": \"kPa\"}", "dedupe_signature": "f4e2ef6998f2b0d0147d4ca4cc2e8a0ce29a9a327bda169c7071c2803074463a", "difficulty": "medium", "final_answer": {"answer": 141.3359, "unit": "kPa"}, "id": "ideal_gas_002703_4.31_467_118.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.31 mol, T=467 K, and V=118.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.31 * 8.314 * 467 / 118.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.31, "temp_k": 467, "volume_l": 118.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=18 degrees through the sine of 2 theta.\n3. Substitute v=64.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 246.1874, \"unit\": \"m\"}", "dedupe_signature": "378987b40332d94e43eb68d5558b70e235f286145dc0d46a9cbe33e59f57089c", "difficulty": "medium", "final_answer": {"answer": 246.1874, "unit": "m"}, "id": "projectile_range_002720_64.1_18", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 64.1 m/s and angle 18 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=18 degrees through the sine of 2 theta.\nSubstitute v=64.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 18, "gravity": 9.81, "speed": 64.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [-0.75, 0.5, 2.15], \"unit\": \"temperature_units\"}", "dedupe_signature": "801f914805b9a7daa9d57dc718634e9c49c7f9970b9b58083f05661ccd81ef0c", "difficulty": "hard", "final_answer": {"answer": [-0.75, 0.5, 2.15], "unit": "temperature_units"}, "id": "heat_step_002729_0.2_1.35_-1.9_0.6_2.6_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.35, right=2.35; current interior values are [-1.9, 0.6, 2.6]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.9, 0.6, 2.6], "left": 1.35, "r": 0.2, "right": 2.35}, "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 = 20.05 kg and a = 6.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 134.335, \"unit\": \"N\"}", "dedupe_signature": "ccbceae60c8e99b4df7be110263bc4ba0cc6b99ea5579480e9916d2abb4a9b26", "difficulty": "easy", "final_answer": {"answer": 134.335, "unit": "N"}, "id": "force_002754_20.05_6.7", "license": "Apache-2.0", "prompt": "A cart has mass 20.05 kg and measured acceleration 6.7 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 = 20.05 kg and a = 6.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.7, "mass": 20.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.2 * 8.314 * 616 / 4.8.\nFinal: {\"answer\": 213.3927, \"unit\": \"kPa\"}", "dedupe_signature": "f2521cf65022c2009cc519da3f387e6fc8e5ff01296c161410bc254cd4a18159", "difficulty": "medium", "final_answer": {"answer": 213.3927, "unit": "kPa"}, "id": "ideal_gas_002757_0.2_616_4.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.2 mol, T=616 K, and V=4.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.2 * 8.314 * 616 / 4.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 0.2, "temp_k": 616, "volume_l": 4.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=226.5 mg, t=357.5 h, and T_half=35.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.2107, \"unit\": \"mg\"}", "dedupe_signature": "144928c3ab25d6afe3025f4c60699c4a5ca23ba9f09768021c9ce8d7d0c32242", "difficulty": "medium", "final_answer": {"answer": 0.2107, "unit": "mg"}, "id": "half_life_002760_226.5_35.5_357.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 226.5 mg. Its half-life is 35.5 hours. How many mg remain after 357.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=226.5 mg, t=357.5 h, and T_half=35.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 357.5, "half_life": 35.5, "initial_amount": 226.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.29 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 953.0252, \"unit\": \"g\"}", "dedupe_signature": "04cafd6ec26d9b0706cfe2bbbf1335f054a42ffb1c25f9c639fbc1664d3d7d0f", "difficulty": "medium", "final_answer": {"answer": 953.0252, "unit": "g"}, "id": "stoich_mass_002761_glucose_5.29", "license": "Apache-2.0", "prompt": "A sample contains 5.29 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 = 5.29 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.29}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3915 mL to 3.915 L.\n3. Compute M = 0.035 / 3.915.\nFinal: {\"answer\": 0.0089, \"unit\": \"mol/L\"}", "dedupe_signature": "0d499416a978fa545024f81054afd4a3c6ac1763cb5e93b5fa8cb2da2509a1ce", "difficulty": "medium", "final_answer": {"answer": 0.0089, "unit": "mol/L"}, "id": "molarity_002762_0.035_3915", "license": "Apache-2.0", "prompt": "A solution contains 0.035 mol of solute in 3915 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3915 mL to 3.915 L.\nCompute M = 0.035 / 3.915.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 0.035, "volume_ml": 3915}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.7, 29.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "290ab2c6420e369fb563d726ec8dc5fc300f086856e242d14847a8f22c532fb2", "difficulty": "medium", "final_answer": {"answer": [4.7, 29.75], "unit": "dimensionless"}, "id": "line_two_point_002768_-5.75_-3.25_4.7_29.75", "license": "Apache-2.0", "prompt": "A line passes through points (-5.75, 2.725) and (-3.25, 14.475). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -5.75, "x2": -3.25, "y1": 2.724999999999998, "y2": 14.475}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7 kg and a = 5.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 38.85, \"unit\": \"N\"}", "dedupe_signature": "5e2dff4643c53b87260dc8b9da35c602a07447123538d99edb0359749acd5106", "difficulty": "easy", "final_answer": {"answer": 38.85, "unit": "N"}, "id": "force_002772_7_5.55", "license": "Apache-2.0", "prompt": "A cart has mass 7 kg and measured acceleration 5.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7 kg and a = 5.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.55, "mass": 7.0}, "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 4690 mL to 4.69 L.\n3. Compute M = 1.815 / 4.69.\nFinal: {\"answer\": 0.387, \"unit\": \"mol/L\"}", "dedupe_signature": "942c07cb955af2ca79a66fd1b782b4c0c880809d939f5497f2d58b02aeaf8fb0", "difficulty": "medium", "final_answer": {"answer": 0.387, "unit": "mol/L"}, "id": "molarity_002780_1.815_4690", "license": "Apache-2.0", "prompt": "A solution contains 1.815 mol of solute in 4690 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4690 mL to 4.69 L.\nCompute M = 1.815 / 4.69.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.815, "volume_ml": 4690}, "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 = 1.46 * 8.314 * 332 / 107.9.\nFinal: {\"answer\": 37.349, \"unit\": \"kPa\"}", "dedupe_signature": "0606cbe3698b4cc938baec1bd47f4d91bacf5f3ddadd50a4cb75ed8aa796c345", "difficulty": "medium", "final_answer": {"answer": 37.349, "unit": "kPa"}, "id": "ideal_gas_002793_1.46_332_107.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.46 mol, T=332 K, and V=107.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.46 * 8.314 * 332 / 107.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.46, "temp_k": 332, "volume_l": 107.9}, "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 = 18.85 kg and a = 3.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 62.205, \"unit\": \"N\"}", "dedupe_signature": "d71d373c9e8c7129182ad44f065e66d1009b805c2bd1f4f56d08da55a0224fca", "difficulty": "easy", "final_answer": {"answer": 62.205, "unit": "N"}, "id": "force_002808_18.85_3.3", "license": "Apache-2.0", "prompt": "A cart has mass 18.85 kg and measured acceleration 3.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.85 kg and a = 3.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.3, "mass": 18.85}, "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=178 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-172.8946, 6.0376], \"unit\": \"N\"}", "dedupe_signature": "4900807d6529d67a414f5d445485aaaefec1540995dbc1be8ad13fd668d3cce3", "difficulty": "medium", "final_answer": {"answer": [-172.8946, 6.0376], "unit": "N"}, "id": "vector_components_002821_173_178", "license": "Apache-2.0", "prompt": "A vector has magnitude 173 N at 178 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=178 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 178, "magnitude": 173.0}, "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: 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": "f14db6b8a310b94b18b2196a2f8ce51c2a96d56eabeb3dcac3430f8a952464fd", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_002825_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each warehouse invoice record from batch 218633 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": "test", "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. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 10618.0 / 1000.\nFinal: {\"answer\": 10.618, \"unit\": \"kg\"}", "dedupe_signature": "93e8f90b71404a75cd81af1cc21e99ed0c222d8673486c4f82678f1bde0bff9a", "difficulty": "easy", "final_answer": {"answer": 10.618, "unit": "kg"}, "id": "unit_convert_002856_g_to_kg_10618", "license": "Apache-2.0", "prompt": "Convert 10618 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 10618.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 10618.0}, "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 = 41.2^2 and multiply by 0.5 * 2.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1909.62, \"unit\": \"J\"}", "dedupe_signature": "53b1e6df7cee7168721e84c4792e6e1f7570eca397b438d2f8b366e930afb0be", "difficulty": "easy", "final_answer": {"answer": 1909.62, "unit": "J"}, "id": "ke_002863_2.25_41.2", "license": "Apache-2.0", "prompt": "A body of mass 2.25 kg moves at 41.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41.2^2 and multiply by 0.5 * 2.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.25, "velocity": 41.2}, "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 2697.0 / 100.\nFinal: {\"answer\": 26.97, \"unit\": \"m\"}", "dedupe_signature": "8b82033eec917d23c0179369e4470bc21b25a4cc1364832e58e32edbef1f09a0", "difficulty": "easy", "final_answer": {"answer": 26.97, "unit": "m"}, "id": "unit_convert_002874_cm_to_m_2697", "license": "Apache-2.0", "prompt": "Convert 2697 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 2697.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 2697.0}, "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\": [-1.75, 17.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "70eb7bfaf8d3fe4bd3e44228b74f838337789cbee99d4ccda3516c8360b05308", "difficulty": "medium", "final_answer": {"answer": [-1.75, 17.0], "unit": "dimensionless"}, "id": "line_two_point_002894_9.5_20.25_-1.75_17", "license": "Apache-2.0", "prompt": "A line passes through points (9.5, 0.375) and (20.25, -18.4375). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 9.5, "x2": 20.25, "y1": 0.375, "y2": -18.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [1.81, 0.4, 0.875], \"unit\": \"temperature_units\"}", "dedupe_signature": "8f7e59e395860ed67b4ba895b97c2e296628cc484e1cc5289b347f48280ad6bd", "difficulty": "hard", "final_answer": {"answer": [1.81, 0.4, 0.875], "unit": "temperature_units"}, "id": "heat_step_002909_0.1_1.6_2.05_0.1_1.15_-0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.6, right=-0.55; current interior values are [2.05, 0.1, 1.15]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [2.05, 0.1, 1.15], "left": 1.6, "r": 0.1, "right": -0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "81cc74fd2da2c7562f00bfe88677e21291be7340407be01b23e93d26a953ea2d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002913_consistent_5ca82cb9_624984", "license": "Apache-2.0", "prompt": "In quality-control check case 624984, 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": "test", "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=75 degrees through the sine of 2 theta.\n3. Substitute v=69.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 248.3201, \"unit\": \"m\"}", "dedupe_signature": "d0ef081c85c3506b5abf609f85c32e27cddc886e3bbc84064b53d0faa892dfc5", "difficulty": "medium", "final_answer": {"answer": 248.3201, "unit": "m"}, "id": "projectile_range_002918_69.8_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 69.8 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=69.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 69.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=32.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 64.667, \"unit\": \"m\"}", "dedupe_signature": "60d4bbbfb63aac1fcaa269b35547acdf294c43ec4baf0f62513894c51fdd3c87", "difficulty": "medium", "final_answer": {"answer": 64.667, "unit": "m"}, "id": "projectile_range_002954_32.1_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 32.1 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=32.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 32.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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 4 steps and round the final state.\nFinal: {\"answer\": 0.384, \"unit\": \"state_units\"}", "dedupe_signature": "3288af491d1af44c03de3b6455cbd5ea453a22dff5a08606407c52d061e60634", "difficulty": "medium", "final_answer": {"answer": 0.384, "unit": "state_units"}, "id": "euler_decay_002979_39.5_0.73_1.8_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.73 y with y(0)=39.5, step size h=1.8, 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) = -0.73 y, so each step multiplies y by 1 - h*0.73.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 39.5, "rate": 0.73, "step": 1.8, "steps": 4}, "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=48 degrees and keep the unit as newtons.\nFinal: {\"answer\": [65.5748, 72.8282], \"unit\": \"N\"}", "dedupe_signature": "1f4a0adb0837ed1176bbbaee3a09ae299c3e17c371d318d6d03da64f30be66b4", "difficulty": "medium", "final_answer": {"answer": [65.5748, 72.8282], "unit": "N"}, "id": "vector_components_003001_98_48", "license": "Apache-2.0", "prompt": "A vector has magnitude 98 N at 48 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=48 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 48, "magnitude": 98.0}, "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 * 246 / 81.4.\nFinal: {\"answer\": 90.9556, \"unit\": \"kPa\"}", "dedupe_signature": "fecd8e05594abd07807adf761b5b9f3593b8b177f71fa9ec3b21c4cc3a109c74", "difficulty": "medium", "final_answer": {"answer": 90.9556, "unit": "kPa"}, "id": "ideal_gas_003009_3.62_246_81.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.62 mol, T=246 K, and V=81.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.62 * 8.314 * 246 / 81.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.62, "temp_k": 246, "volume_l": 81.4}, "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 = 1250 * 3.07 * 17.\nFinal: {\"answer\": 65237.5, \"unit\": \"J\"}", "dedupe_signature": "2d5098692adb487fcc8cf4be453e40949aa62939c578c4181921c8c632f0aaf1", "difficulty": "easy", "final_answer": {"answer": 65237.5, "unit": "J"}, "id": "heat_q_003010_1250_3.07_17", "license": "Apache-2.0", "prompt": "A 1250 g sample has specific heat 3.07 J/(g*K). How much heat is needed to raise its temperature by 17 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1250 * 3.07 * 17.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 17, "heat_capacity": 3.07, "mass_g": 1250}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=114.5 V and R=7.5 ohm.\nFinal: {\"answer\": 1748.0333, \"unit\": \"W\"}", "dedupe_signature": "7afe36df06f02f7f4b86d0e4de6d5fa3a9605261748ce08d1dacfdf86fe22cc5", "difficulty": "easy", "final_answer": {"answer": 1748.0333, "unit": "W"}, "id": "ohm_power_003029_114.5_7.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 7.5 ohm and voltage 114.5 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=114.5 V and R=7.5 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 7.5, "voltage": 114.5}, "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": "187a0165d32960ac30bc90955549cee1e27bd48bce4ae39f14685f2ff21eeb68", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003039_consistent_03f5e041_311445", "license": "Apache-2.0", "prompt": "In instrument manual case 311445, 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": "test", "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 1105 mL to 1.105 L.\n3. Compute M = 1.305 / 1.105.\nFinal: {\"answer\": 1.181, \"unit\": \"mol/L\"}", "dedupe_signature": "99902bbaccf8ad864a21afd710178059ffad9df3a2b7d55fb1abdfdd63e3b387", "difficulty": "medium", "final_answer": {"answer": 1.181, "unit": "mol/L"}, "id": "molarity_003050_1.305_1105", "license": "Apache-2.0", "prompt": "A solution contains 1.305 mol of solute in 1105 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1105 mL to 1.105 L.\nCompute M = 1.305 / 1.105.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.305, "volume_ml": 1105}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(10)=-18.3 and f(18.9)=-30.76.\n3. The interval width is 8.9.\nFinal: {\"answer\": -218.317, \"unit\": \"area_units\"}", "dedupe_signature": "187347e69fee1b80a5f7baa8582141cd02a9eccc7ae84b6a9695d723d8759825", "difficulty": "medium", "final_answer": {"answer": -218.317, "unit": "area_units"}, "id": "trapz_linear_003052_-1.4_-4.3_10_18.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+-4.3 from x=10 to x=18.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(10)=-18.3 and f(18.9)=-30.76.\nThe interval width is 8.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -4.3, "slope": -1.4, "x0": 10.0, "x1": 18.9}, "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=0.26 and add it to the current value.\nFinal: {\"answer\": [0.378, 0.634, 0.465], \"unit\": \"temperature_units\"}", "dedupe_signature": "74f50b5dc991b18c69185a05da7d722e5e078f8187026af8ed07d6bf4a46a50f", "difficulty": "hard", "final_answer": {"answer": [0.378, 0.634, 0.465], "unit": "temperature_units"}, "id": "heat_step_003071_0.26_2.15_-1.65_2.35_-0.25_-0.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.1; current interior values are [-1.65, 2.35, -0.25]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.65, 2.35, -0.25], "left": 2.15, "r": 0.26, "right": -0.1}, "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 = 1.32 * 8.314 * 321 / 17.7.\nFinal: {\"answer\": 199.0287, \"unit\": \"kPa\"}", "dedupe_signature": "be8dc3dc72aadbc7359451877266a1122433edc8c8cd5ddd8f94557e05d766c5", "difficulty": "medium", "final_answer": {"answer": 199.0287, "unit": "kPa"}, "id": "ideal_gas_003081_1.32_321_17.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.32 mol, T=321 K, and V=17.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.32 * 8.314 * 321 / 17.7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.32, "temp_k": 321, "volume_l": 17.7}, "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=89.9 V and R=20.4 ohm.\nFinal: {\"answer\": 396.177, \"unit\": \"W\"}", "dedupe_signature": "1a4d03ce20c65e1cd567633c9abc99ff6f250f60130717aa920bdededa784603", "difficulty": "easy", "final_answer": {"answer": 396.177, "unit": "W"}, "id": "ohm_power_003083_89.9_20.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 20.4 ohm and voltage 89.9 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=89.9 V and R=20.4 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 20.4, "voltage": 89.9}, "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=33 degrees through the sine of 2 theta.\n3. Substitute v=42.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 165.0537, \"unit\": \"m\"}", "dedupe_signature": "bf6ad9b911efd6e5ef1adddc376fc8c9f7b14b4f0d49cfadb57a6a86023216d8", "difficulty": "medium", "final_answer": {"answer": 165.0537, "unit": "m"}, "id": "projectile_range_003098_42.1_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.1 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=42.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 42.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.56 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 256.2227, \"unit\": \"g\"}", "dedupe_signature": "ac4b57b86dcea86a2b95c08375d067bd56bb0445ec6e299ba6f99d680a741ef4", "difficulty": "medium", "final_answer": {"answer": 256.2227, "unit": "g"}, "id": "stoich_mass_003121_calcium_carbonate_2.56", "license": "Apache-2.0", "prompt": "A sample contains 2.56 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 = 2.56 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.56}, "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 204.0 + 273.15.\nFinal: {\"answer\": 477.15, \"unit\": \"K\"}", "dedupe_signature": "a87a98fc6d9ad78b0915b7b3979ca923ed05d918f4fc132aaa6a04b0b1cba53a", "difficulty": "easy", "final_answer": {"answer": 477.15, "unit": "K"}, "id": "unit_convert_003126_c_to_k_204", "license": "Apache-2.0", "prompt": "Convert 204 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 204.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 204.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=678 mg, t=353 h, and T_half=70 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 20.5674, \"unit\": \"mg\"}", "dedupe_signature": "45b96b2cccb195b11f6784fa6db14daa619c27bc1c69c226390aeae7a899f31c", "difficulty": "medium", "final_answer": {"answer": 20.5674, "unit": "mg"}, "id": "half_life_003138_678_70_353", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 678 mg. Its half-life is 70 hours. How many mg remain after 353 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=678 mg, t=353 h, and T_half=70 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 353.0, "half_life": 70.0, "initial_amount": 678.0}, "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)=8.36 and f(6.5)=17.6.\n3. The interval width is 2.1.\nFinal: {\"answer\": 27.258, \"unit\": \"area_units\"}", "dedupe_signature": "4e3c08bb35360c2579115a773c73a28066124911ccb5286d07476e155f7f8c0e", "difficulty": "medium", "final_answer": {"answer": 27.258, "unit": "area_units"}, "id": "trapz_linear_003142_4.4_-11_4.4_6.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+-11 from x=4.4 to x=6.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.4)=8.36 and f(6.5)=17.6.\nThe interval width is 2.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -11.0, "slope": 4.4, "x0": 4.4, "x1": 6.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.2, -25.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "e107f9e180e9a7fe0c7d98425f5a0d6063a16b34fa484e876bbcb8aee1bededb", "difficulty": "medium", "final_answer": {"answer": [-5.2, -25.0], "unit": "dimensionless"}, "id": "line_two_point_003146_-18.5_-12.25_-5.2_-25", "license": "Apache-2.0", "prompt": "A line passes through points (-18.5, 71.2) and (-12.25, 38.7). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -18.5, "x2": -12.25, "y1": 71.2, "y2": 38.7}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=52.7 V and R=102.3 ohm.\nFinal: {\"answer\": 27.1485, \"unit\": \"W\"}", "dedupe_signature": "26bdcf490f9f05e1c49deaf4856004d498342b5f8f990b574779821a356fefb0", "difficulty": "easy", "final_answer": {"answer": 27.1485, "unit": "W"}, "id": "ohm_power_003155_52.7_102.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 102.3 ohm and voltage 52.7 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=52.7 V and R=102.3 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 102.3, "voltage": 52.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3935 mL to 3.935 L.\n3. Compute M = 3.345 / 3.935.\nFinal: {\"answer\": 0.8501, \"unit\": \"mol/L\"}", "dedupe_signature": "e520d8056be8c538fbb6e2c8cd48ad413ec6381d91eb7adef26dc772ed7d242d", "difficulty": "medium", "final_answer": {"answer": 0.8501, "unit": "mol/L"}, "id": "molarity_003158_3.345_3935", "license": "Apache-2.0", "prompt": "A solution contains 3.345 mol of solute in 3935 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3935 mL to 3.935 L.\nCompute M = 3.345 / 3.935.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 3.345, "volume_ml": 3935}, "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 = 3.45^2 and multiply by 0.5 * 7.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 45.2295, \"unit\": \"J\"}", "dedupe_signature": "733db18864058ad31cc471cc64eb031a9575d33f2bbda471ce6e49de11f6775d", "difficulty": "easy", "final_answer": {"answer": 45.2295, "unit": "J"}, "id": "ke_003169_7.6_3.45", "license": "Apache-2.0", "prompt": "A body of mass 7.6 kg moves at 3.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.45^2 and multiply by 0.5 * 7.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.6, "velocity": 3.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.98 * 8.314 * 443 / 16.4.\nFinal: {\"answer\": 1118.4054, \"unit\": \"kPa\"}", "dedupe_signature": "e21574545f27995e254790db65602577ca67e85d4da80b4bbc769d3fb2d55f0d", "difficulty": "medium", "final_answer": {"answer": 1118.4054, "unit": "kPa"}, "id": "ideal_gas_003171_4.98_443_16.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.98 mol, T=443 K, and V=16.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.98 * 8.314 * 443 / 16.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.98, "temp_k": 443, "volume_l": 16.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=158 V and R=88.9 ohm.\nFinal: {\"answer\": 280.8099, \"unit\": \"W\"}", "dedupe_signature": "88787597d2137c05e6618bcc3127d5e8595407fb7cb211b88559703eda28cfb7", "difficulty": "easy", "final_answer": {"answer": 280.8099, "unit": "W"}, "id": "ohm_power_003173_158_88.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 88.9 ohm and voltage 158 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=158 V and R=88.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 88.9, "voltage": 158.0}, "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\": [-1.75, 20.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "ebc642a10cfee9cbea76280ed575b1850d18d02fdaceb6dd25ed7021efd804b8", "difficulty": "medium", "final_answer": {"answer": [-1.75, 20.5], "unit": "dimensionless"}, "id": "line_two_point_003182_-16.25_-10_-1.75_20.5", "license": "Apache-2.0", "prompt": "A line passes through points (-16.25, 48.9375) and (-10, 38). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -16.25, "x2": -10.0, "y1": 48.9375, "y2": 38.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.95 kg and a = 0.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 1.6575, \"unit\": \"N\"}", "dedupe_signature": "23ac1ca08b28e30629a8dabbea320af17bf8fc142e2652dc927c2f16301bf1c3", "difficulty": "easy", "final_answer": {"answer": 1.6575, "unit": "N"}, "id": "force_003186_1.95_0.85", "license": "Apache-2.0", "prompt": "A cart has mass 1.95 kg and measured acceleration 0.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.95 kg and a = 0.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.85, "mass": 1.95}, "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) = -0.04 y, so each step multiplies y by 1 - h*0.04.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 22.1795, \"unit\": \"state_units\"}", "dedupe_signature": "9cf2089de9a908f0c7aa0e8c1909a2bb70d16abc848f1ab642e2cbee58456433", "difficulty": "medium", "final_answer": {"answer": 22.1795, "unit": "state_units"}, "id": "euler_decay_003195_23_0.04_0.45_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.04 y with y(0)=23, step size h=0.45, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 23.0, "rate": 0.04, "step": 0.45, "steps": 2}, "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 = 17.45^2 and multiply by 0.5 * 9.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1423.5492, \"unit\": \"J\"}", "dedupe_signature": "2f2c387c7fc32a3a4ddcc51e8557af2ce002a36cc474cd8ded7a09a472949b11", "difficulty": "easy", "final_answer": {"answer": 1423.5492, "unit": "J"}, "id": "ke_003205_9.35_17.45", "license": "Apache-2.0", "prompt": "A body of mass 9.35 kg moves at 17.45 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 = 17.45^2 and multiply by 0.5 * 9.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.35, "velocity": 17.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.78 * 8.314 * 539 / 105.2.\nFinal: {\"answer\": 203.6156, \"unit\": \"kPa\"}", "dedupe_signature": "99c4f0d3108e9a054f27bea3dd01cbe4d1f5bfa6693c80096036d020113ededc", "difficulty": "medium", "final_answer": {"answer": 203.6156, "unit": "kPa"}, "id": "ideal_gas_003207_4.78_539_105.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.78 mol, T=539 K, and V=105.2 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 = 4.78 * 8.314 * 539 / 105.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.78, "temp_k": 539, "volume_l": 105.2}, "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 = 3.84 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 384.3341, \"unit\": \"g\"}", "dedupe_signature": "c42947c4a70f1936a9dfb1f60025d1889f99a25e84680f361848b4027e2a2c07", "difficulty": "medium", "final_answer": {"answer": 384.3341, "unit": "g"}, "id": "stoich_mass_003211_calcium_carbonate_3.84", "license": "Apache-2.0", "prompt": "A sample contains 3.84 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.84 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.84}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 28.0653, \"unit\": \"state_units\"}", "dedupe_signature": "610f93f375015e930c6447c0fcdad03b7fa157f123033ba00bd2330305c001f0", "difficulty": "medium", "final_answer": {"answer": 28.0653, "unit": "state_units"}, "id": "euler_decay_003213_34_0.01_1.9_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.01 y with y(0)=34, step size h=1.9, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 34.0, "rate": 0.01, "step": 1.9, "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=15 degrees through the sine of 2 theta.\n3. Substitute v=14.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 11.3155, \"unit\": \"m\"}", "dedupe_signature": "ef5202d62111e9cc0febb42cc731bfa4497bbdba48c64a6fce37fa81ff3d086f", "difficulty": "medium", "final_answer": {"answer": 11.3155, "unit": "m"}, "id": "projectile_range_003224_14.9_15", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 14.9 m/s and angle 15 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=15 degrees through the sine of 2 theta.\nSubstitute v=14.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 15, "gravity": 9.81, "speed": 14.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.65 * 8.314 * 554 / 82.4.\nFinal: {\"answer\": 204.026, \"unit\": \"kPa\"}", "dedupe_signature": "741af092942e77cc14bb28b39326da2ddfbe11685b5abc3c0ae79b1cb7b4439f", "difficulty": "medium", "final_answer": {"answer": 204.026, "unit": "kPa"}, "id": "ideal_gas_003225_3.65_554_82.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.65 mol, T=554 K, and V=82.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.65 * 8.314 * 554 / 82.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.65, "temp_k": 554, "volume_l": 82.4}, "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 = 0.01 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1.8016, \"unit\": \"g\"}", "dedupe_signature": "4f507eca8de32aff1ae38744245b066fe5fab7bddeeefad996d954c5fc64eb2d", "difficulty": "medium", "final_answer": {"answer": 1.8016, "unit": "g"}, "id": "stoich_mass_003229_glucose_0.01", "license": "Apache-2.0", "prompt": "A sample contains 0.01 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 = 0.01 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.01}, "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(-9.4)=31.22 and f(-5.4)=22.02.\n3. The interval width is 4.\nFinal: {\"answer\": 106.48, \"unit\": \"area_units\"}", "dedupe_signature": "08a4e5ec6de37566bcfa84b9e9e752093b54fa0943e1b4e528fbca5f6b5fa343", "difficulty": "medium", "final_answer": {"answer": 106.48, "unit": "area_units"}, "id": "trapz_linear_003232_-2.3_9.6_-9.4_-5.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.3x+9.6 from x=-9.4 to x=-5.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.4)=31.22 and f(-5.4)=22.02.\nThe interval width is 4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 9.6, "slope": -2.3, "x0": -9.4, "x1": -5.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [0.86, 0.002, 0.278], \"unit\": \"temperature_units\"}", "dedupe_signature": "5c1c6ebe5adebb9454f239943badbe54d2533301401055b7643669a6ce4715b9", "difficulty": "hard", "final_answer": {"answer": [0.86, 0.002, 0.278], "unit": "temperature_units"}, "id": "heat_step_003233_0.32_2.15_-1.7_2.45_-1.05_-0.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.4; current interior values are [-1.7, 2.45, -1.05]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.7, 2.45, -1.05], "left": 2.15, "r": 0.32, "right": -0.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=341 degrees and keep the unit as newtons.\nFinal: {\"answer\": [34.0387, -11.7205], \"unit\": \"N\"}", "dedupe_signature": "5c13f9dc98b15251233741d0b5071c5413704da3e69a020eb7af9846cfe48ff6", "difficulty": "medium", "final_answer": {"answer": [34.0387, -11.7205], "unit": "N"}, "id": "vector_components_003235_36_341", "license": "Apache-2.0", "prompt": "A vector has magnitude 36 N at 341 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=341 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 341, "magnitude": 36.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.35, -9.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "5abab34fc7d375d37087a992b91aa4fd962863f82e083d3f54ebda85fcb521f0", "difficulty": "medium", "final_answer": {"answer": [7.35, -9.75], "unit": "dimensionless"}, "id": "line_two_point_003236_-15.5_-10_7.35_-9.75", "license": "Apache-2.0", "prompt": "A line passes through points (-15.5, -123.675) and (-10, -83.25). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -15.5, "x2": -10.0, "y1": -123.675, "y2": -83.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.55 kg and a = 14.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 357.2025, \"unit\": \"N\"}", "dedupe_signature": "2860d792c563f5ab186e812dc8217db8777e5b4d53f2ea26d20c761ce2c590c5", "difficulty": "easy", "final_answer": {"answer": 357.2025, "unit": "N"}, "id": "force_003240_24.55_14.55", "license": "Apache-2.0", "prompt": "A cart has mass 24.55 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 = 24.55 kg and a = 14.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.55, "mass": 24.55}, "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=93.5 V and R=7 ohm.\nFinal: {\"answer\": 1248.8929, \"unit\": \"W\"}", "dedupe_signature": "2ae5a89da9be3d13f41686db2c0dff6b0d54d180197e5c8d9d17bcdbc63867ec", "difficulty": "easy", "final_answer": {"answer": 1248.8929, "unit": "W"}, "id": "ohm_power_003245_93.5_7", "license": "Apache-2.0", "prompt": "A resistor has resistance 7 ohm and voltage 93.5 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=93.5 V and R=7 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 7.0, "voltage": 93.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22.0 + 273.15.\nFinal: {\"answer\": 295.15, \"unit\": \"K\"}", "dedupe_signature": "fed4f5f51f7929b0af48caadf777e1671475154f3ba0e600f204917d85f915bc", "difficulty": "easy", "final_answer": {"answer": 295.15, "unit": "K"}, "id": "unit_convert_003252_c_to_k_22", "license": "Apache-2.0", "prompt": "Convert 22 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 22.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 22.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_003274(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_003274\"}", "dedupe_signature": "25e7b453ba61a94589c2290c0d621d216166198a949ff631c9f0abf125ce6f93", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003274"}, "id": "code_003274_clamp_003274", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003274(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": "test", "task_family": "python_code_generation", "variables": {"function": "clamp_003274"}, "verifier": {"function": "clamp_003274", "tests": ["assert clamp_003274(5, 0, 10) == 5", "assert clamp_003274(-2, 0, 10) == 0", "assert clamp_003274(12, 0, 10) == 10", "try:\n    clamp_003274(1, 3, 2)\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 = 2.59 * 8.314 * 321 / 36.0.\nFinal: {\"answer\": 192.0049, \"unit\": \"kPa\"}", "dedupe_signature": "831638bbd9525af6bfcd76803341bc0cbe199cb89df8870d5e2f352acc0a4fe2", "difficulty": "medium", "final_answer": {"answer": 192.0049, "unit": "kPa"}, "id": "ideal_gas_003279_2.59_321_36.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.59 mol, T=321 K, and V=36.0 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 = 2.59 * 8.314 * 321 / 36.0.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.59, "temp_k": 321, "volume_l": 36.0}, "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\": [2.65, -23.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "dca6c14658f651088287ad46fd61e3f21f83df942946e4e6aa2eb4ae246f7c3c", "difficulty": "medium", "final_answer": {"answer": [2.65, -23.25], "unit": "dimensionless"}, "id": "line_two_point_003290_0_2_2.65_-23.25", "license": "Apache-2.0", "prompt": "A line passes through points (0, -23.25) and (2, -17.95). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 0.0, "x2": 2.0, "y1": -23.25, "y2": -17.95}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_003310(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_003310\"}", "dedupe_signature": "4a49e35f612b66fe8d1fd5eea82715ddd452f7f2b4b8a6e4043d4e9354c7bea4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_003310"}, "id": "code_003310_safe_mean_003310", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_003310(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_003310"}, "verifier": {"function": "safe_mean_003310", "tests": ["assert safe_mean_003310([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_003310(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_003310([])\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=56 V and R=178.5 ohm.\nFinal: {\"answer\": 17.5686, \"unit\": \"W\"}", "dedupe_signature": "ef840a555bf244a6ceb800194206633c7b2f65b8f40d8359eabe851ca09a5252", "difficulty": "easy", "final_answer": {"answer": 17.5686, "unit": "W"}, "id": "ohm_power_003317_56_178.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 178.5 ohm and voltage 56 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=56 V and R=178.5 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 178.5, "voltage": 56.0}, "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(3.1)=22.28 and f(5.2)=36.56.\n3. The interval width is 2.1.\nFinal: {\"answer\": 61.782, \"unit\": \"area_units\"}", "dedupe_signature": "d9d59ace73464aabf1e07760a30848d5e207f75974117b2f3dede0769b8857d7", "difficulty": "medium", "final_answer": {"answer": 61.782, "unit": "area_units"}, "id": "trapz_linear_003322_6.8_1.2_3.1_5.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.8x+1.2 from x=3.1 to x=5.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.1)=22.28 and f(5.2)=36.56.\nThe interval width is 2.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 1.2, "slope": 6.8, "x0": 3.1, "x1": 5.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_003328(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_003328\"}", "dedupe_signature": "e9194d47a225203ce4a1c92edc4da5fa42b2ff068453fef7655cd20d3e9015cd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_003328"}, "id": "code_003328_weighted_sum_003328", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_003328(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": "test", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_003328"}, "verifier": {"function": "weighted_sum_003328", "tests": ["assert weighted_sum_003328([2, 3], [4, 5]) == 23", "assert weighted_sum_003328([], []) == 0", "try:\n    weighted_sum_003328([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.45^2 and multiply by 0.5 * 20.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 416.025, \"unit\": \"J\"}", "dedupe_signature": "096078d5f47a7cf520738116e967a6d091a4d9235eb5c29c6e6fd88cd5a33465", "difficulty": "easy", "final_answer": {"answer": 416.025, "unit": "J"}, "id": "ke_003331_20_6.45", "license": "Apache-2.0", "prompt": "A body of mass 20 kg moves at 6.45 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 = 6.45^2 and multiply by 0.5 * 20.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.0, "velocity": 6.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=35 degrees through the sine of 2 theta.\n3. Substitute v=6.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 4.1726, \"unit\": \"m\"}", "dedupe_signature": "c6f4ead24d9cc0f1a5a106e6a22aa12c58c67c2d113cb71ea012a93c30224630", "difficulty": "medium", "final_answer": {"answer": 4.1726, "unit": "m"}, "id": "projectile_range_003332_6.6_35", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 6.6 m/s and angle 35 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=35 degrees through the sine of 2 theta.\nSubstitute v=6.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 35, "gravity": 9.81, "speed": 6.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=13 degrees and keep the unit as newtons.\nFinal: {\"answer\": [401.4405, 92.6798], \"unit\": \"N\"}", "dedupe_signature": "51b30959c4a02c2824962a05516bb09d28d0f4a3aca55a2030aa1743f7168ab5", "difficulty": "medium", "final_answer": {"answer": [401.4405, 92.6798], "unit": "N"}, "id": "vector_components_003361_412_13", "license": "Apache-2.0", "prompt": "A vector has magnitude 412 N at 13 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=13 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 13, "magnitude": 412.0}, "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 = 820 * 1.065 * 104.\nFinal: {\"answer\": 90823.2, \"unit\": \"J\"}", "dedupe_signature": "fd11e65f65c73a4ea211b9033386a91dba472a009ca74c53ed6fefa87a0d64c8", "difficulty": "easy", "final_answer": {"answer": 90823.2, "unit": "J"}, "id": "heat_q_003370_820_1.065_104", "license": "Apache-2.0", "prompt": "A 820 g sample has specific heat 1.065 J/(g*K). How much heat is needed to raise its temperature by 104 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 820 * 1.065 * 104.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 104, "heat_capacity": 1.065, "mass_g": 820}, "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. 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": "eaf7b0dd101589a40398fbe87740671166f806bd778b77db24b6458c669f3520", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003399_consistent_b7d3eed1_607967", "license": "Apache-2.0", "prompt": "In simulation spec case 607967, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.15^2 and multiply by 0.5 * 25.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16.6966, \"unit\": \"J\"}", "dedupe_signature": "c0617c043a803ca4c8c11ce7eb1644522c46ce73faf089a0e82e1f9e8ebcb25b", "difficulty": "easy", "final_answer": {"answer": 16.6966, "unit": "J"}, "id": "ke_003403_25.25_1.15", "license": "Apache-2.0", "prompt": "A body of mass 25.25 kg moves at 1.15 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 = 1.15^2 and multiply by 0.5 * 25.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.25, "velocity": 1.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.26 * 8.314 * 373 / 60.5.\nFinal: {\"answer\": 64.5854, \"unit\": \"kPa\"}", "dedupe_signature": "828d2ea0ad359e79e69baac4ccd18c847557b4db792199f81d453061f98778af", "difficulty": "medium", "final_answer": {"answer": 64.5854, "unit": "kPa"}, "id": "ideal_gas_003405_1.26_373_60.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.26 mol, T=373 K, and V=60.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.26 * 8.314 * 373 / 60.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.26, "temp_k": 373, "volume_l": 60.5}, "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=0.16 and add it to the current value.\nFinal: {\"answer\": [1.938, 0.676, 0.258], \"unit\": \"temperature_units\"}", "dedupe_signature": "a8dd9c852e7c6fb9f04da50390bbd4d9676559a68220436ed1fc2d3460f04907", "difficulty": "hard", "final_answer": {"answer": [1.938, 0.676, 0.258], "unit": "temperature_units"}, "id": "heat_step_003449_0.16_2.05_2.25_0.5_-0.15_1.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.05, right=1.75; current interior values are [2.25, 0.5, -0.15]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [2.25, 0.5, -0.15], "left": 2.05, "r": 0.16, "right": 1.75}, "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 = 15.8 kg and a = 11.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 174.59, \"unit\": \"N\"}", "dedupe_signature": "08e9239cbfb8a3a314b8ad73d25cfdcdedf7c9ef76d192c1d0333f1e7332221b", "difficulty": "easy", "final_answer": {"answer": 174.59, "unit": "N"}, "id": "force_003456_15.8_11.05", "license": "Apache-2.0", "prompt": "A cart has mass 15.8 kg and measured acceleration 11.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.8 kg and a = 11.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.05, "mass": 15.8}, "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) = -0.96 y, so each step multiplies y by 1 - h*0.96.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 11.0088, \"unit\": \"state_units\"}", "dedupe_signature": "b70ecc365f60bdf26b39ea37ca9f622725ee2e499d4449b0f95a29c66a02ddce", "difficulty": "medium", "final_answer": {"answer": 11.0088, "unit": "state_units"}, "id": "euler_decay_003483_30.5_0.96_0.3_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.96 y with y(0)=30.5, step size h=0.3, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 30.5, "rate": 0.96, "step": 0.3, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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": "6be79dd145605efe7d1ff5b24bedbb6d59a00520160a326934427971e503f724", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003489_consistent_b7d3eed1_626983", "license": "Apache-2.0", "prompt": "In field worksheet case 626983, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "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) = -0.15 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\": 9.6109, \"unit\": \"state_units\"}", "dedupe_signature": "5df7aa190dfcd3c46237a70b42aad4cab205f32f9867c7e5c72a06be7ee6c6be", "difficulty": "medium", "final_answer": {"answer": 9.6109, "unit": "state_units"}, "id": "euler_decay_003501_54.5_0.15_1.3_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=54.5, step size h=1.3, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.15 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": "test", "task_family": "numerical_ode", "variables": {"initial_y": 54.5, "rate": 0.15, "step": 1.3, "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=0.02 and add it to the current value.\nFinal: {\"answer\": [-1.029, 2.112, -1.147], \"unit\": \"temperature_units\"}", "dedupe_signature": "949dba55b3e45b1e48cb51fb6b0e45b42df3101bc890734d1b822bb4698010ff", "difficulty": "hard", "final_answer": {"answer": [-1.029, 2.112, -1.147], "unit": "temperature_units"}, "id": "heat_step_003503_0.02_-0.9_-1.1_2.25_-1.3_2.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=2.8; current interior values are [-1.1, 2.25, -1.3]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.1, 2.25, -1.3], "left": -0.9, "r": 0.02, "right": 2.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=107 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-18.2732, 59.769], \"unit\": \"N\"}", "dedupe_signature": "c01988ad6c01ede2b9355321bec88014d73dfb227450678801990973b7c02174", "difficulty": "medium", "final_answer": {"answer": [-18.2732, 59.769], "unit": "N"}, "id": "vector_components_003505_62.5_107", "license": "Apache-2.0", "prompt": "A vector has magnitude 62.5 N at 107 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=107 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 107, "magnitude": 62.5}, "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. Mass equals amount in moles times molar mass.\n2. Use m = 6.91 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 691.6012, \"unit\": \"g\"}", "dedupe_signature": "b1cef79fc3b5000ae801c7777582a190d832ec331be2f8d27bd6cf6f56e87c76", "difficulty": "medium", "final_answer": {"answer": 691.6012, "unit": "g"}, "id": "stoich_mass_003517_calcium_carbonate_6.91", "license": "Apache-2.0", "prompt": "A sample contains 6.91 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 = 6.91 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.91}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1715 mL to 1.715 L.\n3. Compute M = 1.31 / 1.715.\nFinal: {\"answer\": 0.7638, \"unit\": \"mol/L\"}", "dedupe_signature": "62c9b1d1db446098e982159f88c0c5dc15152249cc6c7c9e87b1f3e672453a00", "difficulty": "medium", "final_answer": {"answer": 0.7638, "unit": "mol/L"}, "id": "molarity_003518_1.31_1715", "license": "Apache-2.0", "prompt": "A solution contains 1.31 mol of solute in 1715 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1715 mL to 1.715 L.\nCompute M = 1.31 / 1.715.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.31, "volume_ml": 1715}, "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=54 degrees through the sine of 2 theta.\n3. Substitute v=15.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 22.6945, \"unit\": \"m\"}", "dedupe_signature": "566ef37d45c9f9c87f84ec0337c141bc12efe5c54199a6e536255cc8ec6d1949", "difficulty": "medium", "final_answer": {"answer": 22.6945, "unit": "m"}, "id": "projectile_range_003530_15.3_54", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 15.3 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=54 degrees through the sine of 2 theta.\nSubstitute v=15.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 54, "gravity": 9.81, "speed": 15.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.86 * 8.314 * 268 / 48.5.\nFinal: {\"answer\": 131.3921, \"unit\": \"kPa\"}", "dedupe_signature": "866d2b12589e166c4e3aec9bac1fe70e00060ee50360f67e2a747f2d9fcdf922", "difficulty": "medium", "final_answer": {"answer": 131.3921, "unit": "kPa"}, "id": "ideal_gas_003531_2.86_268_48.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.86 mol, T=268 K, and V=48.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.86 * 8.314 * 268 / 48.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.86, "temp_k": 268, "volume_l": 48.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 995 * 4.465 * 106.\nFinal: {\"answer\": 470923.55, \"unit\": \"J\"}", "dedupe_signature": "f4fc68c8cd38ef7f22c04e849a5cad87e75512e74b705b618662836cd4603008", "difficulty": "easy", "final_answer": {"answer": 470923.55, "unit": "J"}, "id": "heat_q_003532_995_4.465_106", "license": "Apache-2.0", "prompt": "A 995 g sample has specific heat 4.465 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 = 995 * 4.465 * 106.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 106, "heat_capacity": 4.465, "mass_g": 995}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=4.4 V and R=162.1 ohm.\nFinal: {\"answer\": 0.1194, \"unit\": \"W\"}", "dedupe_signature": "5dea2d436f26b7f65e0832999df0700e18ecc9171d98b55f3705f3c2ba9c1999", "difficulty": "easy", "final_answer": {"answer": 0.1194, "unit": "W"}, "id": "ohm_power_003533_4.4_162.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 162.1 ohm and voltage 4.4 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=4.4 V and R=162.1 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 162.1, "voltage": 4.4}, "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=71 degrees through the sine of 2 theta.\n3. Substitute v=8.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 4.6416, \"unit\": \"m\"}", "dedupe_signature": "8454f1fbb643e263220f332a7702045d196ef85eb745fd93b4669225dc6f6bfa", "difficulty": "medium", "final_answer": {"answer": 4.6416, "unit": "m"}, "id": "projectile_range_003566_8.6_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8.6 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=8.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 8.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.81 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 181.1575, \"unit\": \"g\"}", "dedupe_signature": "aabc4a108190660ac5d7bee9abd93ed3705d4a67c114c201c06a5fdf6dad4f60", "difficulty": "medium", "final_answer": {"answer": 181.1575, "unit": "g"}, "id": "stoich_mass_003571_calcium_carbonate_1.81", "license": "Apache-2.0", "prompt": "A sample contains 1.81 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.81 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.81}, "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=221 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-151.3193, -131.5398], \"unit\": \"N\"}", "dedupe_signature": "958395f7ad560377e60372d8dd4761b73a3f3ef2eaf111b6ad0ab0b5c44dbbdd", "difficulty": "medium", "final_answer": {"answer": [-151.3193, -131.5398], "unit": "N"}, "id": "vector_components_003577_200.5_221", "license": "Apache-2.0", "prompt": "A vector has magnitude 200.5 N at 221 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=221 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 221, "magnitude": 200.5}, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=427.5 mg, t=295.5 h, and T_half=119 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 76.4576, \"unit\": \"mg\"}", "dedupe_signature": "2f5a2a0f4620c902f425c9a5ad2faead663a3f6d437019cca7f8bf1144ebe4e7", "difficulty": "medium", "final_answer": {"answer": 76.4576, "unit": "mg"}, "id": "half_life_003588_427.5_119_295.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 427.5 mg. Its half-life is 119 hours. How many mg remain after 295.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=427.5 mg, t=295.5 h, and T_half=119 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 295.5, "half_life": 119.0, "initial_amount": 427.5}, "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 = 3.12 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 312.2714, \"unit\": \"g\"}", "dedupe_signature": "591e044b67d77df4fa96bb7e17ae93c2f85602aef7768a0b009e2542a68b8dc8", "difficulty": "medium", "final_answer": {"answer": 312.2714, "unit": "g"}, "id": "stoich_mass_003589_calcium_carbonate_3.12", "license": "Apache-2.0", "prompt": "A sample contains 3.12 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.12 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.12}, "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=108 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-97.8039, 301.0094], \"unit\": \"N\"}", "dedupe_signature": "fe627b23214a11138cf32687a666dc19f328f140b2bfd3dc4e8051d53f456904", "difficulty": "medium", "final_answer": {"answer": [-97.8039, 301.0094], "unit": "N"}, "id": "vector_components_003595_316.5_108", "license": "Apache-2.0", "prompt": "A vector has magnitude 316.5 N at 108 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=108 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 108, "magnitude": 316.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d9cf61b32da447f31732753b05e245bbef5d27b5b28a9d846f9c688b6736b7f1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003597_inconsistent_1e14b074_211509", "license": "Apache-2.0", "prompt": "In instrument manual case 211509, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * 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=82 degrees through the sine of 2 theta.\n3. Substitute v=41.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 48.6246, \"unit\": \"m\"}", "dedupe_signature": "8c6c303891df62a65645aafeafa3d72cc11e93a917cdcbda255f069ddd333177", "difficulty": "medium", "final_answer": {"answer": 48.6246, "unit": "m"}, "id": "projectile_range_003602_41.6_82", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 41.6 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=82 degrees through the sine of 2 theta.\nSubstitute v=41.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 82, "gravity": 9.81, "speed": 41.6}, "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 = 4.64 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 271.1616, \"unit\": \"g\"}", "dedupe_signature": "d106c121828020bdeba31bdc09ba0b38fb162543e3a43abde38df27d18aaf3c3", "difficulty": "medium", "final_answer": {"answer": 271.1616, "unit": "g"}, "id": "stoich_mass_003607_sodium_chloride_4.64", "license": "Apache-2.0", "prompt": "A sample contains 4.64 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.64 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.64}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3485 mL to 3.485 L.\n3. Compute M = 3.665 / 3.485.\nFinal: {\"answer\": 1.0516, \"unit\": \"mol/L\"}", "dedupe_signature": "6695be8f091859277b6187cc4d19a645b969ac34fc5af48e471fb4699a0b2106", "difficulty": "medium", "final_answer": {"answer": 1.0516, "unit": "mol/L"}, "id": "molarity_003608_3.665_3485", "license": "Apache-2.0", "prompt": "A solution contains 3.665 mol of solute in 3485 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3485 mL to 3.485 L.\nCompute M = 3.665 / 3.485.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 3.665, "volume_ml": 3485}, "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=0.32 and add it to the current value.\nFinal: {\"answer\": [0.602, 0.15, 0.074], \"unit\": \"temperature_units\"}", "dedupe_signature": "d410625e7f016de1891bc8700dc707abfb5a422d41cedacb37bd3054882ce040", "difficulty": "hard", "final_answer": {"answer": [0.602, 0.15, 0.074], "unit": "temperature_units"}, "id": "heat_step_003611_0.32_0.75_-0.55_1.75_-0.95_-0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=-0.45; current interior values are [-0.55, 1.75, -0.95]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.55, 1.75, -0.95], "left": 0.75, "r": 0.32, "right": -0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=280 degrees and keep the unit as newtons.\nFinal: {\"answer\": [35.9452, -203.8552], \"unit\": \"N\"}", "dedupe_signature": "e133f84b01193936c85fe06d33154e9957be03e41034f7a2588dcca05e67b72f", "difficulty": "medium", "final_answer": {"answer": [35.9452, -203.8552], "unit": "N"}, "id": "vector_components_003613_207_280", "license": "Apache-2.0", "prompt": "A vector has magnitude 207 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": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 280, "magnitude": 207.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.2, -13.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "2c627f48b3a1a203536f49b0eb88c4c1cb588f9d52d8f2c60f1f4a758e192357", "difficulty": "medium", "final_answer": {"answer": [1.2, -13.25], "unit": "dimensionless"}, "id": "line_two_point_003614_13.25_14.75_1.2_-13.25", "license": "Apache-2.0", "prompt": "A line passes through points (13.25, 2.65) and (14.75, 4.45). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 13.25, "x2": 14.75, "y1": 2.6499999999999986, "y2": 4.449999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.98 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 351.1998, \"unit\": \"g\"}", "dedupe_signature": "990cc81d6ac4c82ca7c3ae1663eb57afd010559d411344ec7f6762412ced85f5", "difficulty": "medium", "final_answer": {"answer": 351.1998, "unit": "g"}, "id": "stoich_mass_003625_carbon_dioxide_7.98", "license": "Apache-2.0", "prompt": "A sample contains 7.98 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.98 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.98}, "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(9.2)=3.86 and f(14.5)=13.4.\n3. The interval width is 5.3.\nFinal: {\"answer\": 45.739, \"unit\": \"area_units\"}", "dedupe_signature": "8ba2f61981d0268cdd6bdf7e8aafe58d7707ef2b165730a88a8629a4ee19dea9", "difficulty": "medium", "final_answer": {"answer": 45.739, "unit": "area_units"}, "id": "trapz_linear_003628_1.8_-12.7_9.2_14.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.8x+-12.7 from x=9.2 to x=14.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.2)=3.86 and f(14.5)=13.4.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -12.7, "slope": 1.8, "x0": 9.2, "x1": 14.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_003634(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_003634\"}", "dedupe_signature": "07cb4702df66daae80ebd6ba44d6759499a9ced072d7ed473da03cb1ba6ccc50", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_003634"}, "id": "code_003634_pairwise_ratios_003634", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_003634(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": "test", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_003634"}, "verifier": {"function": "pairwise_ratios_003634", "tests": ["assert pairwise_ratios_003634([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_003634([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_003634([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.3 kg and a = 14.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 242.055, \"unit\": \"N\"}", "dedupe_signature": "498c211bdb3eed7505c7d45c8a4fecb824af8bd69caefc6f3e6f24d164d7a337", "difficulty": "easy", "final_answer": {"answer": 242.055, "unit": "N"}, "id": "force_003636_16.3_14.85", "license": "Apache-2.0", "prompt": "A cart has mass 16.3 kg and measured acceleration 14.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.3 kg and a = 14.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.85, "mass": 16.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.1 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 5.844, \"unit\": \"g\"}", "dedupe_signature": "89b5c2c6d715aaab832f09242f4420f49ca0121f9f188272cbb899ad970b69ec", "difficulty": "medium", "final_answer": {"answer": 5.844, "unit": "g"}, "id": "stoich_mass_003643_sodium_chloride_0.1", "license": "Apache-2.0", "prompt": "A sample contains 0.1 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.1 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.1}, "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 = 43.45^2 and multiply by 0.5 * 25.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 23740.3739, \"unit\": \"J\"}", "dedupe_signature": "7519f6696cc050faa3ac06b39a45bfa83d5ce2cb4de7c552f0546d5781bb300a", "difficulty": "easy", "final_answer": {"answer": 23740.3739, "unit": "J"}, "id": "ke_003655_25.15_43.45", "license": "Apache-2.0", "prompt": "A body of mass 25.15 kg moves at 43.45 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 = 43.45^2 and multiply by 0.5 * 25.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.15, "velocity": 43.45}, "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 = 2.06 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 120.3864, \"unit\": \"g\"}", "dedupe_signature": "09a3abcf94e0e69b2bbd27c5510e2c55272dba08fb2c4eadb0d72505c6624d9d", "difficulty": "medium", "final_answer": {"answer": 120.3864, "unit": "g"}, "id": "stoich_mass_003661_sodium_chloride_2.06", "license": "Apache-2.0", "prompt": "A sample contains 2.06 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.06 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.06}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.4 kg and a = 13.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 127.37, \"unit\": \"N\"}", "dedupe_signature": "7d5768640b74a92d6bf46579741efaca8f7f7889ff083fbaabbe40e6a51b4bcf", "difficulty": "easy", "final_answer": {"answer": 127.37, "unit": "N"}, "id": "force_003672_9.4_13.55", "license": "Apache-2.0", "prompt": "A cart has mass 9.4 kg and measured acceleration 13.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.4 kg and a = 13.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.55, "mass": 9.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.09 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 414.3396, \"unit\": \"g\"}", "dedupe_signature": "0cb4ac602f576c75ffdcf170027b1027e40d15279a63ad0102b4d35cf1576f09", "difficulty": "medium", "final_answer": {"answer": 414.3396, "unit": "g"}, "id": "stoich_mass_003679_sodium_chloride_7.09", "license": "Apache-2.0", "prompt": "A sample contains 7.09 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.09 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.09}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2930 mL to 2.93 L.\n3. Compute M = 2.47 / 2.93.\nFinal: {\"answer\": 0.843, \"unit\": \"mol/L\"}", "dedupe_signature": "d7f8a33ca70607dd38922b086c561dc6a3283c08801e12058c32439d41f83c88", "difficulty": "medium", "final_answer": {"answer": 0.843, "unit": "mol/L"}, "id": "molarity_003680_2.47_2930", "license": "Apache-2.0", "prompt": "A solution contains 2.47 mol of solute in 2930 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2930 mL to 2.93 L.\nCompute M = 2.47 / 2.93.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.47, "volume_ml": 2930}, "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 = 3.31 * 8.314 * 348 / 56.2.\nFinal: {\"answer\": 170.4045, \"unit\": \"kPa\"}", "dedupe_signature": "5c479e812696c2b84a556d13449e0975e08a45c41b81d3ca3a02cfc4b1bfe99a", "difficulty": "medium", "final_answer": {"answer": 170.4045, "unit": "kPa"}, "id": "ideal_gas_003693_3.31_348_56.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.31 mol, T=348 K, and V=56.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.31 * 8.314 * 348 / 56.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.31, "temp_k": 348, "volume_l": 56.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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 4888.0 / 100.\nFinal: {\"answer\": 48.88, \"unit\": \"m\"}", "dedupe_signature": "2175d6453bd4577add532faa74dd0a6fcd6b7e13cd54ad94667ad775a6800664", "difficulty": "easy", "final_answer": {"answer": 48.88, "unit": "m"}, "id": "unit_convert_003702_cm_to_m_4888", "license": "Apache-2.0", "prompt": "Convert 4888 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 4888.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 4888.0}, "verifier": {"formula": "value / 100", "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": "7859f0af7abaf513019040f36881a738ffcbb9fe635a7585b45576434aea1e4a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_003707_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile experiment records in release 429910, 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": "test", "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 the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.29 * 8.314 * 353 / 84.3.\nFinal: {\"answer\": 10.0961, \"unit\": \"kPa\"}", "dedupe_signature": "e980bc7eb4778e1e7de17cdf412bdc29171226644739f47475ab2af00b0d6dab", "difficulty": "medium", "final_answer": {"answer": 10.0961, "unit": "kPa"}, "id": "ideal_gas_003711_0.29_353_84.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.29 mol, T=353 K, and V=84.3 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 = 0.29 * 8.314 * 353 / 84.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 0.29, "temp_k": 353, "volume_l": 84.3}, "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(-0.5)=6.55 and f(8.4)=-31.72.\n3. The interval width is 8.9.\nFinal: {\"answer\": -112.0065, \"unit\": \"area_units\"}", "dedupe_signature": "6a0a765c6cf83f0c64c885f6ae8aba0e99d898ea72330fa615f970fd68950fb3", "difficulty": "medium", "final_answer": {"answer": -112.0065, "unit": "area_units"}, "id": "trapz_linear_003718_-4.3_4.4_-0.5_8.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.3x+4.4 from x=-0.5 to x=8.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.5)=6.55 and f(8.4)=-31.72.\nThe interval width is 8.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 4.4, "slope": -4.3, "x0": -0.5, "x1": 8.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 73.0 / 1000.\nFinal: {\"answer\": 0.073, \"unit\": \"kg\"}", "dedupe_signature": "b2807e788987f5542cc54860204b783a638c09df8dd224b18fc17c3456228d66", "difficulty": "easy", "final_answer": {"answer": 0.073, "unit": "kg"}, "id": "unit_convert_003720_g_to_kg_73", "license": "Apache-2.0", "prompt": "Convert 73 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 73.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 73.0}, "verifier": {"formula": "value / 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 13938.0 / 1000.\nFinal: {\"answer\": 13.938, \"unit\": \"kg\"}", "dedupe_signature": "7d3f909f96b286819e51fda03e0654622ded09a2c96f300115655bfe4ed4dc68", "difficulty": "easy", "final_answer": {"answer": 13.938, "unit": "kg"}, "id": "unit_convert_003738_g_to_kg_13938", "license": "Apache-2.0", "prompt": "Convert 13938 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 13938.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 13938.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.35, -4.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "fcaa8093dc291ee03e207405b17c8c33f8180fab8cf4514bae40ff1436c18a3c", "difficulty": "medium", "final_answer": {"answer": [-9.35, -4.0], "unit": "dimensionless"}, "id": "line_two_point_003740_5.25_14.25_-9.35_-4", "license": "Apache-2.0", "prompt": "A line passes through points (5.25, -53.0875) and (14.25, -137.237). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 5.25, "x2": 14.25, "y1": -53.0875, "y2": -137.23749999999998}, "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\": [4.6, 22.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "e9a2b4212ca50277944584bc38e84f135d434ed237a1b1d693faf075213e77be", "difficulty": "medium", "final_answer": {"answer": [4.6, 22.25], "unit": "dimensionless"}, "id": "line_two_point_003758_16.75_30.25_4.6_22.25", "license": "Apache-2.0", "prompt": "A line passes through points (16.75, 99.3) and (30.25, 161.4). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 16.75, "x2": 30.25, "y1": 99.3, "y2": 161.39999999999998}, "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 x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=115 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-154.467, 331.2555], \"unit\": \"N\"}", "dedupe_signature": "a036ef03953cbceff97a82748421244cec20a486332200fd549912a8a86c0231", "difficulty": "medium", "final_answer": {"answer": [-154.467, 331.2555], "unit": "N"}, "id": "vector_components_003775_365.5_115", "license": "Apache-2.0", "prompt": "A vector has magnitude 365.5 N at 115 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=115 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 115, "magnitude": 365.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.65, -3.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "eb931a0f71f306cb8002c5f77784c23a0849b8616912c7fb9690c316692b05ca", "difficulty": "medium", "final_answer": {"answer": [-0.65, -3.25], "unit": "dimensionless"}, "id": "line_two_point_003794_-18.75_-5_-0.65_-3.25", "license": "Apache-2.0", "prompt": "A line passes through points (-18.75, 8.9375) and (-5, 0). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -18.75, "x2": -5.0, "y1": 8.9375, "y2": 0.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.97 * 8.314 * 525 / 97.0.\nFinal: {\"answer\": 133.6454, \"unit\": \"kPa\"}", "dedupe_signature": "3803268334d01a3f6e5f7e1bf8d4296b939fab4e9a5a2c303449e0f37fbff0f0", "difficulty": "medium", "final_answer": {"answer": 133.6454, "unit": "kPa"}, "id": "ideal_gas_003801_2.97_525_97.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.97 mol, T=525 K, and V=97.0 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 = 2.97 * 8.314 * 525 / 97.0.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.97, "temp_k": 525, "volume_l": 97.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=6 degrees and keep the unit as newtons.\nFinal: {\"answer\": [171.0578, 17.9789], \"unit\": \"N\"}", "dedupe_signature": "048694c7c3c2f4edf87237ad7c954bb6244d9e31b0e3d4e55bc4867be423afc5", "difficulty": "medium", "final_answer": {"answer": [171.0578, 17.9789], "unit": "N"}, "id": "vector_components_003811_172_6", "license": "Apache-2.0", "prompt": "A vector has magnitude 172 N at 6 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=6 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 6, "magnitude": 172.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.55, -24.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "c4b77f6650ec0d9fb3a76e0cf2c7bfab7a838e99a654c4dd6bcacc57fcf59439", "difficulty": "medium", "final_answer": {"answer": [-1.55, -24.75], "unit": "dimensionless"}, "id": "line_two_point_003812_-0.5_5.75_-1.55_-24.75", "license": "Apache-2.0", "prompt": "A line passes through points (-0.5, -23.975) and (5.75, -33.6625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -0.5, "x2": 5.75, "y1": -23.975, "y2": -33.6625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "b026c79b870a7a670e42947228d53b65bd42d00a3dd37f67bfe00ec70e6b5b39", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003833_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=67.5 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": "test", "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 slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.3, -9.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "795405450fb7a72d02d2cfea8b0ea3cb8f29f58a66d4e96ea7f155b004f4e8a5", "difficulty": "medium", "final_answer": {"answer": [-1.3, -9.25], "unit": "dimensionless"}, "id": "line_two_point_003848_-4.75_3_-1.3_-9.25", "license": "Apache-2.0", "prompt": "A line passes through points (-4.75, -3.075) and (3, -13.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -4.75, "x2": 3.0, "y1": -3.075, "y2": -13.15}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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\": 8.4085, \"unit\": \"state_units\"}", "dedupe_signature": "a6a68c246b93fccceac615bf8f8e8a7e7dc7121bdafe69caa4392ef73ed89b3f", "difficulty": "medium", "final_answer": {"answer": 8.4085, "unit": "state_units"}, "id": "euler_decay_003861_28_0.86_1.8_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.86 y with y(0)=28, step size h=1.8, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.86 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": "test", "task_family": "numerical_ode", "variables": {"initial_y": 28.0, "rate": 0.86, "step": 1.8, "steps": 2}, "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=197.5 V and R=199.2 ohm.\nFinal: {\"answer\": 195.8145, \"unit\": \"W\"}", "dedupe_signature": "280e1407446a54c73a01c23c7e702d07fa5090facd902a66ffbd7ec78d759f6e", "difficulty": "easy", "final_answer": {"answer": 195.8145, "unit": "W"}, "id": "ohm_power_003875_197.5_199.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 199.2 ohm and voltage 197.5 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=197.5 V and R=199.2 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 199.2, "voltage": 197.5}, "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=37 degrees through the sine of 2 theta.\n3. Substitute v=16.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 27.9863, \"unit\": \"m\"}", "dedupe_signature": "a0094546d57332f47721ebb500c795a0c18bd67bcc513ae76216ca4c1849564c", "difficulty": "medium", "final_answer": {"answer": 27.9863, "unit": "m"}, "id": "projectile_range_003890_16.9_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 16.9 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=16.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 16.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "e0ad1240c5d678c7d18a42a83484a946c57fd904e616db5b7f4d548e33eaee48", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003941_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 58.9 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": "test", "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=630 mg, t=84.5 h, and T_half=9.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.3236, \"unit\": \"mg\"}", "dedupe_signature": "ed8ade28fb3cae6b5b4bbba93a621a953b4d583effbd95b306a87c5e2dec1c8c", "difficulty": "medium", "final_answer": {"answer": 1.3236, "unit": "mg"}, "id": "half_life_003948_630_9.5_84.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 630 mg. Its half-life is 9.5 hours. How many mg remain after 84.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=630 mg, t=84.5 h, and T_half=9.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 84.5, "half_life": 9.5, "initial_amount": 630.0}, "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_003958(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_003958\"}", "dedupe_signature": "b4e52284373ce14a8d255b27263adfbdd4cdd9a77deb4d03047ab0792ffce8a0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003958"}, "id": "code_003958_clamp_003958", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003958(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": "test", "task_family": "python_code_generation", "variables": {"function": "clamp_003958"}, "verifier": {"function": "clamp_003958", "tests": ["assert clamp_003958(5, 0, 10) == 5", "assert clamp_003958(-2, 0, 10) == 0", "assert clamp_003958(12, 0, 10) == 10", "try:\n    clamp_003958(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.5 kg and a = 9.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 161.0, \"unit\": \"N\"}", "dedupe_signature": "ff430558e8e13eaded86a6445c4f4d9cc61b9172239ad307028b5e9a9e14f771", "difficulty": "easy", "final_answer": {"answer": 161.0, "unit": "N"}, "id": "force_003960_17.5_9.2", "license": "Apache-2.0", "prompt": "A cart has mass 17.5 kg and measured acceleration 9.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.5 kg and a = 9.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.2, "mass": 17.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 33.45^2 and multiply by 0.5 * 20.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11636.586, \"unit\": \"J\"}", "dedupe_signature": "cb11245e06f5aaa6dc34cb0d93a629e5e94c6943bb5a753a468f0f2b131f9aec", "difficulty": "easy", "final_answer": {"answer": 11636.586, "unit": "J"}, "id": "ke_003961_20.8_33.45", "license": "Apache-2.0", "prompt": "A body of mass 20.8 kg moves at 33.45 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 = 33.45^2 and multiply by 0.5 * 20.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.8, "velocity": 33.45}, "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 = 11.5 kg and a = 13.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 155.25, \"unit\": \"N\"}", "dedupe_signature": "249c315f314891d334a30a1ef449ca5f615a3a442ee04dc65e56aae83a25bb3c", "difficulty": "easy", "final_answer": {"answer": 155.25, "unit": "N"}, "id": "force_003978_11.5_13.5", "license": "Apache-2.0", "prompt": "A cart has mass 11.5 kg and measured acceleration 13.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.5 kg and a = 13.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.5, "mass": 11.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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, -21.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "6a1dc8e8a491eaf6837371e37d2868f3020ed3d701c8c4789ccdd9c682963fe4", "difficulty": "medium", "final_answer": {"answer": [-5.65, -21.5], "unit": "dimensionless"}, "id": "line_two_point_003992_-0.25_13.5_-5.65_-21.5", "license": "Apache-2.0", "prompt": "A line passes through points (-0.25, -20.0875) and (13.5, -97.775). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -0.25, "x2": 13.5, "y1": -20.0875, "y2": -97.775}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=73 degrees through the sine of 2 theta.\n3. Substitute v=19.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 20.795, \"unit\": \"m\"}", "dedupe_signature": "343d5de906bbd4fdc42bbae7af84374411b675cdbc6f27808d71a074ce45a69f", "difficulty": "medium", "final_answer": {"answer": 20.795, "unit": "m"}, "id": "projectile_range_004016_19.1_73", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 19.1 m/s and angle 73 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=73 degrees through the sine of 2 theta.\nSubstitute v=19.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 73, "gravity": 9.81, "speed": 19.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=10 mg, t=345.5 h, and T_half=67.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.2879, \"unit\": \"mg\"}", "dedupe_signature": "02c52e1b237a7360f7e82c302853c1c403250c896c9de3b25955c5083e8502ac", "difficulty": "medium", "final_answer": {"answer": 0.2879, "unit": "mg"}, "id": "half_life_004020_10_67.5_345.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 10 mg. Its half-life is 67.5 hours. How many mg remain after 345.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=10 mg, t=345.5 h, and T_half=67.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 345.5, "half_life": 67.5, "initial_amount": 10.0}, "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\": [-4.5, -15.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c78904bc25a63fc4767bbd8cf67fac9f504738fda0ebb81f43d34b3f03af2002", "difficulty": "medium", "final_answer": {"answer": [-4.5, -15.25], "unit": "dimensionless"}, "id": "line_two_point_004028_9.5_19.75_-4.5_-15.25", "license": "Apache-2.0", "prompt": "A line passes through points (9.5, -58) and (19.75, -104.125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 9.5, "x2": 19.75, "y1": -58.0, "y2": -104.125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.97 y, so each step multiplies y by 1 - h*0.97.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": -5.7474, \"unit\": \"state_units\"}", "dedupe_signature": "53abd0691a2225f7fadffbbab8dab4fd057d52ed83aea843adf5b51ffc242d2c", "difficulty": "medium", "final_answer": {"answer": -5.7474, "unit": "state_units"}, "id": "euler_decay_004077_13.5_0.97_1.9_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.97 y with y(0)=13.5, step size h=1.9, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.97 y, so each step multiplies y by 1 - h*0.97.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 13.5, "rate": 0.97, "step": 1.9, "steps": 5}, "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=120 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-48.25, 83.5715], \"unit\": \"N\"}", "dedupe_signature": "c35d8e51afdad4ec24ad20c9169e44f2c136b10a5015fe5ea73eba868cb8f41c", "difficulty": "medium", "final_answer": {"answer": [-48.25, 83.5715], "unit": "N"}, "id": "vector_components_004099_96.5_120", "license": "Apache-2.0", "prompt": "A vector has magnitude 96.5 N at 120 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=120 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 120, "magnitude": 96.5}, "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 = 14.35 kg and a = 5.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 76.7725, \"unit\": \"N\"}", "dedupe_signature": "57ee5c3476102a28cf21a658ba7be1b4c815781af22736ca16b302619466a459", "difficulty": "easy", "final_answer": {"answer": 76.7725, "unit": "N"}, "id": "force_004104_14.35_5.35", "license": "Apache-2.0", "prompt": "A cart has mass 14.35 kg and measured acceleration 5.35 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 = 14.35 kg and a = 5.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.35, "mass": 14.35}, "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 = 1625 * 1.12 * 66.\nFinal: {\"answer\": 120120.0, \"unit\": \"J\"}", "dedupe_signature": "f2b54482a1f7438b812cbf80a49e39baee559f407647b7b55d73507037a9db6f", "difficulty": "easy", "final_answer": {"answer": 120120.0, "unit": "J"}, "id": "heat_q_004108_1625_1.12_66", "license": "Apache-2.0", "prompt": "A 1625 g sample has specific heat 1.12 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 = 1625 * 1.12 * 66.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 66, "heat_capacity": 1.12, "mass_g": 1625}, "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=0.02 and add it to the current value.\nFinal: {\"answer\": [-0.869, -1.196, 1.086], \"unit\": \"temperature_units\"}", "dedupe_signature": "65ad7eca97130f2fd74e4b65d60958532451587c9ddf0d432f75a629b1359fc1", "difficulty": "hard", "final_answer": {"answer": [-0.869, -1.196, 1.086], "unit": "temperature_units"}, "id": "heat_step_004115_0.02_1.0_-0.9_-1.25_1.1_2.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=2.75; current interior values are [-0.9, -1.25, 1.1]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.9, -1.25, 1.1], "left": 1.0, "r": 0.02, "right": 2.75}, "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=55 degrees through the sine of 2 theta.\n3. Substitute v=46.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 205.3425, \"unit\": \"m\"}", "dedupe_signature": "eedabad843530eaa3441cc2a6efe98d4db1871220d94ee92b8825faaf9d11047", "difficulty": "medium", "final_answer": {"answer": 205.3425, "unit": "m"}, "id": "projectile_range_004124_46.3_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 46.3 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=55 degrees through the sine of 2 theta.\nSubstitute v=46.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "gravity": 9.81, "speed": 46.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "5dec8dac71887a83d119367d1509e50b48c8e7f2dd8760813a59a35f7cd4ee4a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004137_inconsistent_1e14b074_383356", "license": "Apache-2.0", "prompt": "In field worksheet case 383356, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4295 mL to 4.295 L.\n3. Compute M = 3.355 / 4.295.\nFinal: {\"answer\": 0.7811, \"unit\": \"mol/L\"}", "dedupe_signature": "4b9222d8cfef448fd69db30fc788410b5b90293c22f6eb0c36d64d9b64be0719", "difficulty": "medium", "final_answer": {"answer": 0.7811, "unit": "mol/L"}, "id": "molarity_004148_3.355_4295", "license": "Apache-2.0", "prompt": "A solution contains 3.355 mol of solute in 4295 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4295 mL to 4.295 L.\nCompute M = 3.355 / 4.295.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 3.355, "volume_ml": 4295}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "25bdbb97dd795461b2f97f1cf17783919b826158142150fe4d08318acac1c869", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004149_59_0.81_1.3_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.81 y with y(0)=59, step size h=1.3, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 59.0, "rate": 0.81, "step": 1.3, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3)=6.8 and f(9.2)=-10.56.\n3. The interval width is 6.2.\nFinal: {\"answer\": -11.656, \"unit\": \"area_units\"}", "dedupe_signature": "d414ba521d4ffebf401a0831125a522f9c4538abd8514a612df1b64cac61bf36", "difficulty": "medium", "final_answer": {"answer": -11.656, "unit": "area_units"}, "id": "trapz_linear_004186_-2.8_15.2_3_9.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+15.2 from x=3 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(3)=6.8 and f(9.2)=-10.56.\nThe interval width is 6.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 15.2, "slope": -2.8, "x0": 3.0, "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. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=118 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-71.8291, 135.091], \"unit\": \"N\"}", "dedupe_signature": "345fd18834a2d4855788ea14e2cb72e23daa38a21483fb44f1506062a2e30b25", "difficulty": "medium", "final_answer": {"answer": [-71.8291, 135.091], "unit": "N"}, "id": "vector_components_004207_153_118", "license": "Apache-2.0", "prompt": "A vector has magnitude 153 N at 118 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=118 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 118, "magnitude": 153.0}, "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 3861.0 / 100.\nFinal: {\"answer\": 38.61, \"unit\": \"m\"}", "dedupe_signature": "58e09e8ccb6bd0afaa75d10a8c0de05a8d85776bfd3a29615aa0202ef84782e3", "difficulty": "easy", "final_answer": {"answer": 38.61, "unit": "m"}, "id": "unit_convert_004224_cm_to_m_3861", "license": "Apache-2.0", "prompt": "Convert 3861 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 3861.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 3861.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=25 degrees and keep the unit as newtons.\nFinal: {\"answer\": [224.3112, 104.598], \"unit\": \"N\"}", "dedupe_signature": "bc68c061e5b772e5e365f6fdc0ef102819579f21a2a3f73f3c0ddfaeab098c5b", "difficulty": "medium", "final_answer": {"answer": [224.3112, 104.598], "unit": "N"}, "id": "vector_components_004225_247.5_25", "license": "Apache-2.0", "prompt": "A vector has magnitude 247.5 N at 25 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=25 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 25, "magnitude": 247.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.8, 22.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "dccd560417e7501dff942960a0db43a332ccffadffb0beec8096886d5f2e1575", "difficulty": "medium", "final_answer": {"answer": [-6.8, 22.75], "unit": "dimensionless"}, "id": "line_two_point_004226_-9_-3.5_-6.8_22.75", "license": "Apache-2.0", "prompt": "A line passes through points (-9, 83.95) and (-3.5, 46.55). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -9.0, "x2": -3.5, "y1": 83.94999999999999, "y2": 46.55}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4100 mL to 4.1 L.\n3. Compute M = 4.18 / 4.1.\nFinal: {\"answer\": 1.0195, \"unit\": \"mol/L\"}", "dedupe_signature": "7d5d00bafa4aa86b4d0ba57e8ad8fdb389cda50f32d047606e89f0b5fc50420c", "difficulty": "medium", "final_answer": {"answer": 1.0195, "unit": "mol/L"}, "id": "molarity_004238_4.18_4100", "license": "Apache-2.0", "prompt": "A solution contains 4.18 mol of solute in 4100 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4100 mL to 4.1 L.\nCompute M = 4.18 / 4.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.18, "volume_ml": 4100}, "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 = 6.56 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 656.5707, \"unit\": \"g\"}", "dedupe_signature": "c5f050cec8bf47a5da8ca6bd0c328dafa1cb26e54a9f24cef8500553d5ae6a80", "difficulty": "medium", "final_answer": {"answer": 656.5707, "unit": "g"}, "id": "stoich_mass_004255_calcium_carbonate_6.56", "license": "Apache-2.0", "prompt": "A sample contains 6.56 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 = 6.56 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.56}, "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 = 5.7^2 and multiply by 0.5 * 13.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 218.4952, \"unit\": \"J\"}", "dedupe_signature": "d97732684e910e21a0ea1805a3d7a8e22078ee245b2ee61c991daacb30fbb93e", "difficulty": "easy", "final_answer": {"answer": 218.4952, "unit": "J"}, "id": "ke_004267_13.45_5.7", "license": "Apache-2.0", "prompt": "A body of mass 13.45 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 * 13.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.45, "velocity": 5.7}, "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) = -0.8 y, so each step multiplies y by 1 - h*0.8.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.015, \"unit\": \"state_units\"}", "dedupe_signature": "a89e1cc36a5720fb7983c32a2f60c195424c6d62aa534a418652dd675b9cb81b", "difficulty": "medium", "final_answer": {"answer": 0.015, "unit": "state_units"}, "id": "euler_decay_004275_14_0.8_1.65_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.8 y with y(0)=14, step size h=1.65, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 14.0, "rate": 0.8, "step": 1.65, "steps": 6}, "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=231 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-140.3384, -173.3035], \"unit\": \"N\"}", "dedupe_signature": "77b5ab557e11030a422b22d98d2b61f1247598103449aace2da76e988058f4fa", "difficulty": "medium", "final_answer": {"answer": [-140.3384, -173.3035], "unit": "N"}, "id": "vector_components_004279_223_231", "license": "Apache-2.0", "prompt": "A vector has magnitude 223 N at 231 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=231 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 231, "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. 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": "541182cc1216d029e9e3b480799e4e55981310f00a63609181216dc6d9fb667f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004281_consistent_03f5e041_498299", "license": "Apache-2.0", "prompt": "In sensor calibration case 498299, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "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) = -0.31 y, so each step multiplies y by 1 - h*0.31.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0003, \"unit\": \"state_units\"}", "dedupe_signature": "2591893a965f4957b2d3aad5af8ab1c8311bb78df061ace57647fdfd27906b4a", "difficulty": "medium", "final_answer": {"answer": 0.0003, "unit": "state_units"}, "id": "euler_decay_004311_38.5_0.31_2_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.31 y with y(0)=38.5, step size h=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) = -0.31 y, so each step multiplies y by 1 - h*0.31.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 38.5, "rate": 0.31, "step": 2.0, "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. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "743e3c8e3c6215cd77209be92ab5fcbe2f4728479a0d88772bf3622011ea090a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004317_inconsistent_1e14b074_869793", "license": "Apache-2.0", "prompt": "In student derivation case 869793, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.05 kg and a = 11.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 70.4825, \"unit\": \"N\"}", "dedupe_signature": "3b3424dd6e0329b9cccd96abbaef416dda14980ec5d2cf0407feae5fe3b59a30", "difficulty": "easy", "final_answer": {"answer": 70.4825, "unit": "N"}, "id": "force_004320_6.05_11.65", "license": "Apache-2.0", "prompt": "A cart has mass 6.05 kg and measured acceleration 11.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.05 kg and a = 11.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.65, "mass": 6.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.44 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 7.9266, \"unit\": \"g\"}", "dedupe_signature": "2bd839f2573f7673164541031562fd2e16c7b88a6b73d3dc49119b9e7ce9a876", "difficulty": "medium", "final_answer": {"answer": 7.9266, "unit": "g"}, "id": "stoich_mass_004327_water_0.44", "license": "Apache-2.0", "prompt": "A sample contains 0.44 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.44 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.44}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1010 mL to 1.01 L.\n3. Compute M = 1.45 / 1.01.\nFinal: {\"answer\": 1.4356, \"unit\": \"mol/L\"}", "dedupe_signature": "b01d8222fa079bf67db6d4b90a94ac6d25d2dee9d5241d96d4015c61e119689f", "difficulty": "medium", "final_answer": {"answer": 1.4356, "unit": "mol/L"}, "id": "molarity_004328_1.45_1010", "license": "Apache-2.0", "prompt": "A solution contains 1.45 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 = 1.45 / 1.01.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.45, "volume_ml": 1010}, "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 = 18.2 kg and a = 7.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 132.86, \"unit\": \"N\"}", "dedupe_signature": "e6568054246cb9b7cf539a6350cb50f5707edc300553b192cb61d8ada07ebb71", "difficulty": "easy", "final_answer": {"answer": 132.86, "unit": "N"}, "id": "force_004338_18.2_7.3", "license": "Apache-2.0", "prompt": "A cart has mass 18.2 kg and measured acceleration 7.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.2 kg and a = 7.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.3, "mass": 18.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.8^2 and multiply by 0.5 * 15.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 15107.715, \"unit\": \"J\"}", "dedupe_signature": "df9e961223af6fac550f6f8fb63861095c48ad6c3c4dc900402360a022ff04ae", "difficulty": "easy", "final_answer": {"answer": 15107.715, "unit": "J"}, "id": "ke_004339_15.75_43.8", "license": "Apache-2.0", "prompt": "A body of mass 15.75 kg moves at 43.8 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 = 43.8^2 and multiply by 0.5 * 15.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.75, "velocity": 43.8}, "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=100 V and R=78.5 ohm.\nFinal: {\"answer\": 127.3885, \"unit\": \"W\"}", "dedupe_signature": "7e0a0a2c62557bad3e01961324e8ed6993fcab9373043d8d99c7b6229d29453b", "difficulty": "easy", "final_answer": {"answer": 127.3885, "unit": "W"}, "id": "ohm_power_004343_100_78.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 78.5 ohm and voltage 100 V across it. Compute the dissipated power 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 V and R=78.5 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 78.5, "voltage": 100.0}, "verifier": {"formula": "voltage ** 2 / resistance", "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 249.5 + 273.15.\nFinal: {\"answer\": 522.65, \"unit\": \"K\"}", "dedupe_signature": "262268ce6536fff37759f3e936c78f615f57556a7e353cc33ffda26f2a402770", "difficulty": "easy", "final_answer": {"answer": 522.65, "unit": "K"}, "id": "unit_convert_004350_c_to_k_249.5", "license": "Apache-2.0", "prompt": "Convert 249.5 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 249.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 249.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ac10cb4c3e2fe3c122d3333331d2b32775242d7d68df7bafc5af7c24e34d3312", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004353_consistent_4153435f_60851", "license": "Apache-2.0", "prompt": "In quality-control check case 60851, 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": "test", "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 = 285 * 3.845 * 79.\nFinal: {\"answer\": 86570.175, \"unit\": \"J\"}", "dedupe_signature": "0847bedd3f3fc80a89a8c6e62c9c71e638c751552e18d6ad1ce228f454121438", "difficulty": "easy", "final_answer": {"answer": 86570.175, "unit": "J"}, "id": "heat_q_004360_285_3.845_79", "license": "Apache-2.0", "prompt": "A 285 g sample has specific heat 3.845 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 = 285 * 3.845 * 79.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 3.845, "mass_g": 285}, "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": "9b97087ff6d5a67b8c1e81423265ca419355fddb4f69f539bb43c1c8e77423c9", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004391_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 27.3 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": "test", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.55 kg and a = 11.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 208.6875, \"unit\": \"N\"}", "dedupe_signature": "fc8b42aec55970fa80775b3548a86cd3ce779641a81a3aa2d6789b5d57cd5b68", "difficulty": "easy", "final_answer": {"answer": 208.6875, "unit": "N"}, "id": "force_004392_18.55_11.25", "license": "Apache-2.0", "prompt": "A cart has mass 18.55 kg and measured acceleration 11.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.55 kg and a = 11.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.25, "mass": 18.55}, "verifier": {"formula": "mass * acceleration", "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 3788.0 / 100.\nFinal: {\"answer\": 37.88, \"unit\": \"m\"}", "dedupe_signature": "8864f960c1342590376189356b01f3386959e940754194a5bdf3e654c440d6a8", "difficulty": "easy", "final_answer": {"answer": 37.88, "unit": "m"}, "id": "unit_convert_004404_cm_to_m_3788", "license": "Apache-2.0", "prompt": "Convert 3788 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 3788.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 3788.0}, "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=0.6 V and R=59.1 ohm.\nFinal: {\"answer\": 0.0061, \"unit\": \"W\"}", "dedupe_signature": "679c6036062af9b699106189ddd82499a0251c6bc02ea3760f9dbf4c8a1af415", "difficulty": "easy", "final_answer": {"answer": 0.0061, "unit": "W"}, "id": "ohm_power_004433_0.6_59.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 59.1 ohm and voltage 0.6 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=0.6 V and R=59.1 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 59.1, "voltage": 0.6}, "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) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 6.3967, \"unit\": \"state_units\"}", "dedupe_signature": "e87a1cc4b8992aeff701b5233e5da19bcf6197764471bce97325f7d312d985ec", "difficulty": "medium", "final_answer": {"answer": 6.3967, "unit": "state_units"}, "id": "euler_decay_004437_7.5_0.03_1.3_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=7.5, 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) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 7.5, "rate": 0.03, "step": 1.3, "steps": 4}, "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 4003.5 / 100.\nFinal: {\"answer\": 40.035, \"unit\": \"m\"}", "dedupe_signature": "9cc86a3b329e69210b2b24d970b6756fb116e3ce31d1093f512a69397960d619", "difficulty": "easy", "final_answer": {"answer": 40.035, "unit": "m"}, "id": "unit_convert_004440_cm_to_m_4003.5", "license": "Apache-2.0", "prompt": "Convert 4003.5 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 4003.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 4003.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=213 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-257.4719, -167.2042], \"unit\": \"N\"}", "dedupe_signature": "542668eb25de76f37a8c737437bebef61c3e39e6b46aa942e36c9e16af0347b7", "difficulty": "medium", "final_answer": {"answer": [-257.4719, -167.2042], "unit": "N"}, "id": "vector_components_004441_307_213", "license": "Apache-2.0", "prompt": "A vector has magnitude 307 N at 213 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=213 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 213, "magnitude": 307.0}, "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. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.65^2 and multiply by 0.5 * 22.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 22777.1371, \"unit\": \"J\"}", "dedupe_signature": "b1c64ee70adeb683646978fc0349652a9811a962220b90e08c658d6435da9e99", "difficulty": "easy", "final_answer": {"answer": 22777.1371, "unit": "J"}, "id": "ke_004447_22.85_44.65", "license": "Apache-2.0", "prompt": "A body of mass 22.85 kg moves at 44.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.65^2 and multiply by 0.5 * 22.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.85, "velocity": 44.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.01 * 8.314 * 469 / 75.8.\nFinal: {\"answer\": 154.8389, \"unit\": \"kPa\"}", "dedupe_signature": "6cac10401d25fbbde06917249dbd1c3052a74ecf06aed7dc8ac987356d523568", "difficulty": "medium", "final_answer": {"answer": 154.8389, "unit": "kPa"}, "id": "ideal_gas_004467_3.01_469_75.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.01 mol, T=469 K, and V=75.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.01 * 8.314 * 469 / 75.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.01, "temp_k": 469, "volume_l": 75.8}, "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. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "712f5a7cbb9726ba362562047198aa7f590da383ebc1226dcd95c5e5e8158558", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004479_consistent_03f5e041_40051", "license": "Apache-2.0", "prompt": "In lab notebook case 40051, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"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 * 15.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7878.4734, \"unit\": \"J\"}", "dedupe_signature": "46ef4fd4a05befb3622e590b4bf50485bc0be35e00f71aa0d5b904ecc2b73088", "difficulty": "easy", "final_answer": {"answer": 7878.4734, "unit": "J"}, "id": "ke_004483_15.15_32.25", "license": "Apache-2.0", "prompt": "A body of mass 15.15 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 * 15.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.15, "velocity": 32.25}, "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 2885 mL to 2.885 L.\n3. Compute M = 1.7 / 2.885.\nFinal: {\"answer\": 0.5893, \"unit\": \"mol/L\"}", "dedupe_signature": "624efeb2ec17dd98d3bb115daeebc1792cbb5f2db33710e34d7e8db663d97fc2", "difficulty": "medium", "final_answer": {"answer": 0.5893, "unit": "mol/L"}, "id": "molarity_004508_1.7_2885", "license": "Apache-2.0", "prompt": "A solution contains 1.7 mol of solute in 2885 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2885 mL to 2.885 L.\nCompute M = 1.7 / 2.885.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.7, "volume_ml": 2885}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.2)=-0.8 and f(-1.1)=-0.5.\n3. The interval width is 0.1.\nFinal: {\"answer\": -0.065, \"unit\": \"area_units\"}", "dedupe_signature": "de0beeb47bd9626dfb429e7d7dddd9c04f6d7818d1aa5a8ea6e5fddb665092cd", "difficulty": "medium", "final_answer": {"answer": -0.065, "unit": "area_units"}, "id": "trapz_linear_004510_3_2.8_-1.2_-1.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3x+2.8 from x=-1.2 to x=-1.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.2)=-0.8 and f(-1.1)=-0.5.\nThe interval width is 0.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 2.8, "slope": 3.0, "x0": -1.2, "x1": -1.0999999999999999}, "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\": [-6.9, 7.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "b8e56ff9e3e833ed99da7c4b98050f2eeda1b61ec3e66d34000513b1fb428148", "difficulty": "medium", "final_answer": {"answer": [-6.9, 7.75], "unit": "dimensionless"}, "id": "line_two_point_004514_11.75_26_-6.9_7.75", "license": "Apache-2.0", "prompt": "A line passes through points (11.75, -73.325) and (26, -171.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 11.75, "x2": 26.0, "y1": -73.325, "y2": -171.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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=25.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 27.1722, \"unit\": \"m\"}", "dedupe_signature": "3c3984d3723de0fa2ad2e377ad978ae22f4130d5563d082743ce351b9dfaab65", "difficulty": "medium", "final_answer": {"answer": 27.1722, "unit": "m"}, "id": "projectile_range_004538_25.6_78", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 25.6 m/s and angle 78 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=78 degrees through the sine of 2 theta.\nSubstitute v=25.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 78, "gravity": 9.81, "speed": 25.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.68 * 8.314 * 277 / 117.1.\nFinal: {\"answer\": 33.0402, \"unit\": \"kPa\"}", "dedupe_signature": "40731a9b8906bf0c932b330fe968630737982afc5e5810eb1ddd6b10ca77e2c3", "difficulty": "medium", "final_answer": {"answer": 33.0402, "unit": "kPa"}, "id": "ideal_gas_004557_1.68_277_117.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.68 mol, T=277 K, and V=117.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.68 * 8.314 * 277 / 117.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.68, "temp_k": 277, "volume_l": 117.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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 -76.5 + 273.15.\nFinal: {\"answer\": 196.65, \"unit\": \"K\"}", "dedupe_signature": "c8de73e35b5a9a72217657f2621a840ed83a9dc7f7974c9d44b592896a5b0313", "difficulty": "easy", "final_answer": {"answer": 196.65, "unit": "K"}, "id": "unit_convert_004566_c_to_k_-76.5", "license": "Apache-2.0", "prompt": "Convert -76.5 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 -76.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": -76.5}, "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 = 16.05 kg and a = 12.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 203.835, \"unit\": \"N\"}", "dedupe_signature": "72362f3573ca045cd911ee055d256c4351767af464bbc79d9fb7192bf3c131d0", "difficulty": "easy", "final_answer": {"answer": 203.835, "unit": "N"}, "id": "force_004572_16.05_12.7", "license": "Apache-2.0", "prompt": "A cart has mass 16.05 kg and measured acceleration 12.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.05 kg and a = 12.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.7, "mass": 16.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.72 * 8.314 * 412 / 64.0.\nFinal: {\"answer\": 199.0995, \"unit\": \"kPa\"}", "dedupe_signature": "b1252433810977df004e2b82a3edad12728ca9615ba9939eaab4501bad0be181", "difficulty": "medium", "final_answer": {"answer": 199.0995, "unit": "kPa"}, "id": "ideal_gas_004575_3.72_412_64.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.72 mol, T=412 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 = 3.72 * 8.314 * 412 / 64.0.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.72, "temp_k": 412, "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. 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": "c03fa5bb56fdc5ada9da5b50bc4d7e3dc18ec8e94e6201eb7f8528f8406449ad", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004605_consistent_03f5e041_503118", "license": "Apache-2.0", "prompt": "In field worksheet case 503118, 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": "test", "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: 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": "1761527c57175f21620a1aedc4035b1d21a037efb26d5f33da6c850cba61e20d", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004625_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory survey record from batch 53825 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": "test", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=48 degrees through the sine of 2 theta.\n3. Substitute v=40.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 169.5868, \"unit\": \"m\"}", "dedupe_signature": "ced04450eb1f7f779defc2b694da91e552884e703dc4f62efdd87cb7ed876851", "difficulty": "medium", "final_answer": {"answer": 169.5868, "unit": "m"}, "id": "projectile_range_004628_40.9_48", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.9 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=40.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 48, "gravity": 9.81, "speed": 40.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=226.3 V and R=146.8 ohm.\nFinal: {\"answer\": 348.8535, \"unit\": \"W\"}", "dedupe_signature": "be3e1c39a7dd28057ad0e8065c6babe0cc229818dcb1e7067ed473db658f145b", "difficulty": "easy", "final_answer": {"answer": 348.8535, "unit": "W"}, "id": "ohm_power_004631_226.3_146.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 146.8 ohm and voltage 226.3 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=226.3 V and R=146.8 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 146.8, "voltage": 226.3}, "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(9.2)=-18.14 and f(14.7)=-32.99.\n3. The interval width is 5.5.\nFinal: {\"answer\": -140.6075, \"unit\": \"area_units\"}", "dedupe_signature": "c5aa98934f6f4b5a2545c385d0a03e2f87970ae5b82c3ad8d9202576a3b563ea", "difficulty": "medium", "final_answer": {"answer": -140.6075, "unit": "area_units"}, "id": "trapz_linear_004636_-2.7_6.7_9.2_14.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+6.7 from x=9.2 to x=14.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.2)=-18.14 and f(14.7)=-32.99.\nThe interval width is 5.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 6.7, "slope": -2.7, "x0": 9.2, "x1": 14.7}, "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=217 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-132.1742, -99.6004], \"unit\": \"N\"}", "dedupe_signature": "b7c31961240b7173bcfe1971c3610ec9bb8b65bafe01abd2213df4d587342900", "difficulty": "medium", "final_answer": {"answer": [-132.1742, -99.6004], "unit": "N"}, "id": "vector_components_004639_165.5_217", "license": "Apache-2.0", "prompt": "A vector has magnitude 165.5 N at 217 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=217 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 217, "magnitude": 165.5}, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=607.5 mg, t=358 h, and T_half=35 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.5063, \"unit\": \"mg\"}", "dedupe_signature": "38cf74ad099bf9b7218571dae0b9d5e7245811863a01f530f3fb3fa957cfa10f", "difficulty": "medium", "final_answer": {"answer": 0.5063, "unit": "mg"}, "id": "half_life_004650_607.5_35_358", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 607.5 mg. Its half-life is 35 hours. How many mg remain after 358 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=607.5 mg, t=358 h, and T_half=35 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 358.0, "half_life": 35.0, "initial_amount": 607.5}, "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. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "17812053e8232ab7027f6a37894ebbaef0d7544a36e142a967d8d2fee393255b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004659_inconsistent_74ac0b02_445467", "license": "Apache-2.0", "prompt": "In sensor calibration case 445467, 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": "test", "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=36 degrees through the sine of 2 theta.\n3. Substitute v=41.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 170.2023, \"unit\": \"m\"}", "dedupe_signature": "24630bfd477955a454b65d9d4dc65ec91e9132a599d4c1aade28312199e3ca8a", "difficulty": "medium", "final_answer": {"answer": 170.2023, "unit": "m"}, "id": "projectile_range_004664_41.9_36", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 41.9 m/s and angle 36 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=36 degrees through the sine of 2 theta.\nSubstitute v=41.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 36, "gravity": 9.81, "speed": 41.9}, "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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.1)=18.85 and f(3)=9.7.\n3. The interval width is 6.1.\nFinal: {\"answer\": 87.0775, \"unit\": \"area_units\"}", "dedupe_signature": "555abd2fa73bc5bf4ba25d34ba60bff620d47765b735ee0b3a6eaae2ae1e9db1", "difficulty": "medium", "final_answer": {"answer": 87.0775, "unit": "area_units"}, "id": "trapz_linear_004672_-1.5_14.2_-3.1_3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+14.2 from x=-3.1 to x=3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.1)=18.85 and f(3)=9.7.\nThe interval width is 6.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 14.2, "slope": -1.5, "x0": -3.1, "x1": 2.9999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22348.0 / 1000.\nFinal: {\"answer\": 22.348, \"unit\": \"kg\"}", "dedupe_signature": "23f9459632e68ee589ce2227055d9b69d1c9a5510b9d4a133dab72305946a3d8", "difficulty": "easy", "final_answer": {"answer": 22.348, "unit": "kg"}, "id": "unit_convert_004674_g_to_kg_22348", "license": "Apache-2.0", "prompt": "Convert 22348 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 22348.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 22348.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3885 mL to 3.885 L.\n3. Compute M = 2.045 / 3.885.\nFinal: {\"answer\": 0.5264, \"unit\": \"mol/L\"}", "dedupe_signature": "a91637a8526c24a8327b1a9c36e03be1780e85369fd8fcaa98b10af4428f11a4", "difficulty": "medium", "final_answer": {"answer": 0.5264, "unit": "mol/L"}, "id": "molarity_004688_2.045_3885", "license": "Apache-2.0", "prompt": "A solution contains 2.045 mol of solute in 3885 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3885 mL to 3.885 L.\nCompute M = 2.045 / 3.885.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.045, "volume_ml": 3885}, "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 = 4.34 * 8.314 * 553 / 55.6.\nFinal: {\"answer\": 358.8807, \"unit\": \"kPa\"}", "dedupe_signature": "657561e6817acf8770b979d969043b64823add743e2358324758c9665b7f0723", "difficulty": "medium", "final_answer": {"answer": 358.8807, "unit": "kPa"}, "id": "ideal_gas_004701_4.34_553_55.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.34 mol, T=553 K, and V=55.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.34 * 8.314 * 553 / 55.6.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.34, "temp_k": 553, "volume_l": 55.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=183.5 V and R=176.9 ohm.\nFinal: {\"answer\": 190.3462, \"unit\": \"W\"}", "dedupe_signature": "0178afe520ac3461fde4bcb263a2bacc43e2505e8612e32652f136bf433af91c", "difficulty": "easy", "final_answer": {"answer": 190.3462, "unit": "W"}, "id": "ohm_power_004703_183.5_176.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 176.9 ohm and voltage 183.5 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=183.5 V and R=176.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 176.9, "voltage": 183.5}, "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) = -0.55 y, so each step multiplies y by 1 - h*0.55.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 30.65, \"unit\": \"state_units\"}", "dedupe_signature": "9ffd8010e01ffcc25aa3f1127653795048ce7f8909764feab8c0548e4cc265d4", "difficulty": "medium", "final_answer": {"answer": 30.65, "unit": "state_units"}, "id": "euler_decay_004725_56_0.55_0.15_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.55 y with y(0)=56, step size h=0.15, 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) = -0.55 y, so each step multiplies y by 1 - h*0.55.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 56.0, "rate": 0.55, "step": 0.15, "steps": 7}, "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=10.7 V and R=135.9 ohm.\nFinal: {\"answer\": 0.8425, \"unit\": \"W\"}", "dedupe_signature": "87e15dff6e52c69ffa76ebe85d52989d69e6aeddcfb4a717dcff38710c0a9e6b", "difficulty": "easy", "final_answer": {"answer": 0.8425, "unit": "W"}, "id": "ohm_power_004739_10.7_135.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 135.9 ohm and voltage 10.7 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=10.7 V and R=135.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 135.9, "voltage": 10.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=383 mg, t=95.5 h, and T_half=23 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 21.5412, \"unit\": \"mg\"}", "dedupe_signature": "934e7d51c5eeb352b0470c36cffbadd18216064a305911df4ac58692def8fa23", "difficulty": "medium", "final_answer": {"answer": 21.5412, "unit": "mg"}, "id": "half_life_004740_383_23_95.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 383 mg. Its half-life is 23 hours. How many mg remain after 95.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=383 mg, t=95.5 h, and T_half=23 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 95.5, "half_life": 23.0, "initial_amount": 383.0}, "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 safe_mean_004750(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_004750\"}", "dedupe_signature": "094df19ea06b7ef6d0537692bf94b1b8214452c596282aeb98158c200306f46a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004750"}, "id": "code_004750_safe_mean_004750", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004750(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004750"}, "verifier": {"function": "safe_mean_004750", "tests": ["assert safe_mean_004750([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004750(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004750([])\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 = 1865 * 0.695 * 100.\nFinal: {\"answer\": 129617.5, \"unit\": \"J\"}", "dedupe_signature": "aa6838c4c8f2f137aa1e37c8789b4cd5c19f41144ffdd7589114a166718972f6", "difficulty": "easy", "final_answer": {"answer": 129617.5, "unit": "J"}, "id": "heat_q_004756_1865_0.695_100", "license": "Apache-2.0", "prompt": "A 1865 g sample has specific heat 0.695 J/(g*K). How much heat is needed to raise its temperature by 100 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1865 * 0.695 * 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 100, "heat_capacity": 0.695, "mass_g": 1865}, "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) = -0.22 y, so each step multiplies y by 1 - h*0.22.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 1.7965, \"unit\": \"state_units\"}", "dedupe_signature": "b89ebbcc51181a4aa015bfdb4bcddb0e2cbbf5db3b7c91b37945378e37843f09", "difficulty": "medium", "final_answer": {"answer": 1.7965, "unit": "state_units"}, "id": "euler_decay_004761_37_0.22_1.8_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.22 y with y(0)=37, step size h=1.8, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.22 y, so each step multiplies y by 1 - h*0.22.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 37.0, "rate": 0.22, "step": 1.8, "steps": 6}, "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_004768(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_004768\"}", "dedupe_signature": "a3fb49097c961bf8fa2a79f22632b5c6745475e2836c3d2c878e3a64b9911993", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004768"}, "id": "code_004768_safe_mean_004768", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004768(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004768"}, "verifier": {"function": "safe_mean_004768", "tests": ["assert safe_mean_004768([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004768(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004768([])\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 = 4.15 * 8.314 * 556 / 71.4.\nFinal: {\"answer\": 268.6796, \"unit\": \"kPa\"}", "dedupe_signature": "90376be4ce725c6248fe2b05c1a37d6a37fe7f13599ce619e8a2446506641aec", "difficulty": "medium", "final_answer": {"answer": 268.6796, "unit": "kPa"}, "id": "ideal_gas_004773_4.15_556_71.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.15 mol, T=556 K, and V=71.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.15 * 8.314 * 556 / 71.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.15, "temp_k": 556, "volume_l": 71.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=737.5 mg, t=233 h, and T_half=4.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "8e0b40d134de5e90815e72895e7eea678cf480624e3099eff442a247ab2f4cac", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_004776_737.5_4.5_233", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 737.5 mg. Its half-life is 4.5 hours. How many mg remain after 233 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=737.5 mg, t=233 h, and T_half=4.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 233.0, "half_life": 4.5, "initial_amount": 737.5}, "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 4725 mL to 4.725 L.\n3. Compute M = 4.17 / 4.725.\nFinal: {\"answer\": 0.8825, \"unit\": \"mol/L\"}", "dedupe_signature": "ee902d8a13e300a0e6e99f89431cf462a9c70fcd841859fc2e84f4cd54ed41cf", "difficulty": "medium", "final_answer": {"answer": 0.8825, "unit": "mol/L"}, "id": "molarity_004778_4.17_4725", "license": "Apache-2.0", "prompt": "A solution contains 4.17 mol of solute in 4725 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4725 mL to 4.725 L.\nCompute M = 4.17 / 4.725.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.17, "volume_ml": 4725}, "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 safe_mean_004786(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_004786\"}", "dedupe_signature": "8c02ab2ac0a0c90428329b742485e1c54a854f5c2a7207293de39d707bcb8af3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004786"}, "id": "code_004786_safe_mean_004786", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004786(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004786"}, "verifier": {"function": "safe_mean_004786", "tests": ["assert safe_mean_004786([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004786(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004786([])\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 = 9.55^2 and multiply by 0.5 * 22.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1044.2686, \"unit\": \"J\"}", "dedupe_signature": "cfec4294ce1fa36f6fbbcb9afee652261b978629ca010660bb97ed3b00f828c1", "difficulty": "easy", "final_answer": {"answer": 1044.2686, "unit": "J"}, "id": "ke_004807_22.9_9.55", "license": "Apache-2.0", "prompt": "A body of mass 22.9 kg moves at 9.55 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 = 9.55^2 and multiply by 0.5 * 22.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.9, "velocity": 9.55}, "verifier": {"formula": "0.5 * mass * velocity ** 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: 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": "531bdbc2c62db9ba594f64f3b1fc3dcc9a4b3ccf429717c1abb1da59b79cf33d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004823_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=8 and h=1.05, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "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. 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": "e9887f7c40aa0e6e4776bee8fa8d094668b3ac9e7f16f5fda0f711a4edce99ce", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004839_consistent_741d4e34_419600", "license": "Apache-2.0", "prompt": "In quality-control check case 419600, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "c811a3c50db6693dd43422b5817139e8f865cc16acc16cd0eaf066ae0a80a1e5", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004859_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.53 mol and T=349 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": "test", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "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 = 385 * 1.7 * 53.\nFinal: {\"answer\": 34688.5, \"unit\": \"J\"}", "dedupe_signature": "afa6dd733791b1d00d4cb3afda9adcf5d11f41b959a191ea214578d5a8135ef9", "difficulty": "easy", "final_answer": {"answer": 34688.5, "unit": "J"}, "id": "heat_q_004882_385_1.7_53", "license": "Apache-2.0", "prompt": "A 385 g sample has specific heat 1.7 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 = 385 * 1.7 * 53.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 53, "heat_capacity": 1.7, "mass_g": 385}, "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: 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": "dcb1076a015b1f10aebbc1b6d02c2260a01454e39d3a729d3cdc37251570ee9a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_004895_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field crop records in release 374960, 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": "test", "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2920 mL to 2.92 L.\n3. Compute M = 0.12 / 2.92.\nFinal: {\"answer\": 0.0411, \"unit\": \"mol/L\"}", "dedupe_signature": "93d35eb887a3deaf6d861e094361a68f9cc1affedc096306328e1f38a7d2a05d", "difficulty": "medium", "final_answer": {"answer": 0.0411, "unit": "mol/L"}, "id": "molarity_004976_0.12_2920", "license": "Apache-2.0", "prompt": "A solution contains 0.12 mol of solute in 2920 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2920 mL to 2.92 L.\nCompute M = 0.12 / 2.92.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 0.12, "volume_ml": 2920}, "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=0.04 and add it to the current value.\nFinal: {\"answer\": [-1.028, 1.854, 2.66], \"unit\": \"temperature_units\"}", "dedupe_signature": "9ce5345e37c8da94195193a77bf8e0483a82d1006ab1be335446a79cb18d75bd", "difficulty": "hard", "final_answer": {"answer": [-1.028, 1.854, 2.66], "unit": "temperature_units"}, "id": "heat_step_004979_0.04_-0.05_-1.2_1.95_2.7_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=-0.05, right=2.45; current interior values are [-1.2, 1.95, 2.7]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.2, 1.95, 2.7], "left": -0.05, "r": 0.04, "right": 2.45}, "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: 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": "9b636c1c7d766edca0205ff8fa6852c67329a9c43ca608ff7bbffb7477144e05", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_004985_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field experiment records in release 395122, 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": "test", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=21 degrees through the sine of 2 theta.\n3. Substitute v=81 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 447.5195, \"unit\": \"m\"}", "dedupe_signature": "f2f30237912d60133adacd90dba5b7ac0ee6e335f577c3e31a33d2a5e5d10016", "difficulty": "medium", "final_answer": {"answer": 447.5195, "unit": "m"}, "id": "projectile_range_004988_81_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81 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=81 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "gravity": 9.81, "speed": 81.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4730 mL to 4.73 L.\n3. Compute M = 1.95 / 4.73.\nFinal: {\"answer\": 0.4123, \"unit\": \"mol/L\"}", "dedupe_signature": "5e517c1c592868e3de4d0443f8b8ec50d127270b99cba3da71cc65ce8075e144", "difficulty": "medium", "final_answer": {"answer": 0.4123, "unit": "mol/L"}, "id": "molarity_004994_1.95_4730", "license": "Apache-2.0", "prompt": "A solution contains 1.95 mol of solute in 4730 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4730 mL to 4.73 L.\nCompute M = 1.95 / 4.73.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.95, "volume_ml": 4730}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 3.4579, \"unit\": \"state_units\"}", "dedupe_signature": "12677b33e6794c5301c7a0adffe77aa2b16504da4f4bb53024fd5865353ef1e1", "difficulty": "medium", "final_answer": {"answer": 3.4579, "unit": "state_units"}, "id": "euler_decay_004995_66.5_0.2_1.4_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.2 y with y(0)=66.5, step size h=1.4, 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) = -0.2 y, so each step multiplies y by 1 - h*0.2.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 66.5, "rate": 0.2, "step": 1.4, "steps": 9}, "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 -36.0 + 273.15.\nFinal: {\"answer\": 237.15, \"unit\": \"K\"}", "dedupe_signature": "041cbc060ae613cab97be938c20775bfa10579f1e567ecc879d1cfdcd356de31", "difficulty": "easy", "final_answer": {"answer": 237.15, "unit": "K"}, "id": "unit_convert_004998_c_to_k_-36", "license": "Apache-2.0", "prompt": "Convert -36 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -36.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": -36.0}, "verifier": {"formula": "value + 273.15", "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": "8ca1075b6db0d7c6f724dcb48ca222bdca7c538666b304c6fc93f152fd00eebe", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_005003_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=24 and h=0.5, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "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 = 2.79 * 8.314 * 242 / 103.1.\nFinal: {\"answer\": 54.4466, \"unit\": \"kPa\"}", "dedupe_signature": "bf3a45844a486016e4b763b5683569652938917712fd500e20577d308d6f9ce9", "difficulty": "medium", "final_answer": {"answer": 54.4466, "unit": "kPa"}, "id": "ideal_gas_005007_2.79_242_103.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.79 mol, T=242 K, and V=103.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.79 * 8.314 * 242 / 103.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.79, "temp_k": 242, "volume_l": 103.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 530 * 1.1 * 47.\nFinal: {\"answer\": 27401.0, \"unit\": \"J\"}", "dedupe_signature": "55739536c21d20e480e5ad55da26e7f00b84e046167d6757504380ca3adc294d", "difficulty": "easy", "final_answer": {"answer": 27401.0, "unit": "J"}, "id": "heat_q_005026_530_1.1_47", "license": "Apache-2.0", "prompt": "A 530 g sample has specific heat 1.1 J/(g*K). How much heat is needed to raise its temperature by 47 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 530 * 1.1 * 47.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 47, "heat_capacity": 1.1, "mass_g": 530}, "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=5 degrees through the sine of 2 theta.\n3. Substitute v=5.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 0.4972, \"unit\": \"m\"}", "dedupe_signature": "cade302321c3049296504dfa8da592d4095e61635172ec069bea1509539f535d", "difficulty": "medium", "final_answer": {"answer": 0.4972, "unit": "m"}, "id": "projectile_range_005042_5.3_5", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 5.3 m/s and angle 5 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=5 degrees through the sine of 2 theta.\nSubstitute v=5.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 5, "gravity": 9.81, "speed": 5.3}, "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=80.8 V and R=176.5 ohm.\nFinal: {\"answer\": 36.9895, \"unit\": \"W\"}", "dedupe_signature": "a994a01fa71f209aa5746580645d8dbd8fc0c57065e55c2c4357cdae63c2909b", "difficulty": "easy", "final_answer": {"answer": 36.9895, "unit": "W"}, "id": "ohm_power_005045_80.8_176.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 176.5 ohm and voltage 80.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=80.8 V and R=176.5 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 176.5, "voltage": 80.8}, "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\": [-5.35, 11.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "365007630c7d9a18bb1d9238e571c51255a835f076d7e4db5a5ae8ba8ec7c8e8", "difficulty": "medium", "final_answer": {"answer": [-5.35, 11.25], "unit": "dimensionless"}, "id": "line_two_point_005054_6.75_9_-5.35_11.25", "license": "Apache-2.0", "prompt": "A line passes through points (6.75, -24.8625) and (9, -36.9). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 6.75, "x2": 9.0, "y1": -24.862499999999997, "y2": -36.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_005056(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_005056\"}", "dedupe_signature": "15855a48a21259246dceae17929278e6e6e88f76defba5e14b4e507c8f3c8495", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005056"}, "id": "code_005056_clamp_005056", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005056(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": "test", "task_family": "python_code_generation", "variables": {"function": "clamp_005056"}, "verifier": {"function": "clamp_005056", "tests": ["assert clamp_005056(5, 0, 10) == 5", "assert clamp_005056(-2, 0, 10) == 0", "assert clamp_005056(12, 0, 10) == 10", "try:\n    clamp_005056(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 = 30.8^2 and multiply by 0.5 * 10.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5027.792, \"unit\": \"J\"}", "dedupe_signature": "0d8e431b907a6d3018e86263eeee5bd9896d8c729d93f0e01bee3e017bd32e7e", "difficulty": "easy", "final_answer": {"answer": 5027.792, "unit": "J"}, "id": "ke_005059_10.6_30.8", "license": "Apache-2.0", "prompt": "A body of mass 10.6 kg moves at 30.8 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 = 30.8^2 and multiply by 0.5 * 10.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.6, "velocity": 30.8}, "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 = 7.93 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 348.9993, \"unit\": \"g\"}", "dedupe_signature": "04e4c21284dd4db8f85d42bdfe8f46c54fc62801e5f82a66b5271fc573b5d102", "difficulty": "medium", "final_answer": {"answer": 348.9993, "unit": "g"}, "id": "stoich_mass_005083_carbon_dioxide_7.93", "license": "Apache-2.0", "prompt": "A sample contains 7.93 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 = 7.93 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.93}, "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=203 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-297.3231, -126.2062], \"unit\": \"N\"}", "dedupe_signature": "24a676cf5539d933af25589d0aa9def58989ff568bbb9b4bb732a5978af79959", "difficulty": "medium", "final_answer": {"answer": [-297.3231, -126.2062], "unit": "N"}, "id": "vector_components_005089_323_203", "license": "Apache-2.0", "prompt": "A vector has magnitude 323 N at 203 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=203 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 203, "magnitude": 323.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.25, 0.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "8cfcc7e246cc3d460d35c1359c901568f7ed9534f2435490f9880b1f981b7866", "difficulty": "medium", "final_answer": {"answer": [-4.25, 0.25], "unit": "dimensionless"}, "id": "line_two_point_005090_14_18.25_-4.25_0.25", "license": "Apache-2.0", "prompt": "A line passes through points (14, -59.25) and (18.25, -77.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 14.0, "x2": 18.25, "y1": -59.25, "y2": -77.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4645 mL to 4.645 L.\n3. Compute M = 4.76 / 4.645.\nFinal: {\"answer\": 1.0248, \"unit\": \"mol/L\"}", "dedupe_signature": "85964b7e843d30aad7d43f09f790ef0313c1ce27169e2587d1158c845f0343bb", "difficulty": "medium", "final_answer": {"answer": 1.0248, "unit": "mol/L"}, "id": "molarity_005102_4.76_4645", "license": "Apache-2.0", "prompt": "A solution contains 4.76 mol of solute in 4645 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4645 mL to 4.645 L.\nCompute M = 4.76 / 4.645.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.76, "volume_ml": 4645}, "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": "23ac6333b59635e685a7ffa80d3369f4fdfde5dd8b72916705bb5e0504607b8a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005111_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each warehouse ledger record from batch 691332 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": "test", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.32 * 8.314 * 586 / 18.1.\nFinal: {\"answer\": 624.4779, \"unit\": \"kPa\"}", "dedupe_signature": "bfc191fec9cf2a434a27c455f58e5cd42bf76a4dbb90c9d098ff4dd63aaddbf8", "difficulty": "medium", "final_answer": {"answer": 624.4779, "unit": "kPa"}, "id": "ideal_gas_005115_2.32_586_18.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.32 mol, T=586 K, and V=18.1 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 = 2.32 * 8.314 * 586 / 18.1.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.32, "temp_k": 586, "volume_l": 18.1}, "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 4960 mL to 4.96 L.\n3. Compute M = 2.025 / 4.96.\nFinal: {\"answer\": 0.4083, \"unit\": \"mol/L\"}", "dedupe_signature": "c76bf799d4815502bcda3f708238c9cbb51233187c3507ad9860da1bfe3b51c0", "difficulty": "medium", "final_answer": {"answer": 0.4083, "unit": "mol/L"}, "id": "molarity_005120_2.025_4960", "license": "Apache-2.0", "prompt": "A solution contains 2.025 mol of solute in 4960 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4960 mL to 4.96 L.\nCompute M = 2.025 / 4.96.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.025, "volume_ml": 4960}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.8, -11.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "a0901633a2e6ee765ccc7fbbb3f7fbe393cb441c29c16a2723510570d8a90a3c", "difficulty": "medium", "final_answer": {"answer": [4.8, -11.25], "unit": "dimensionless"}, "id": "line_two_point_005126_12_15.75_4.8_-11.25", "license": "Apache-2.0", "prompt": "A line passes through points (12, 46.35) and (15.75, 64.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 12.0, "x2": 15.75, "y1": 46.349999999999994, "y2": 64.35}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=137 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-177.7189, 165.7256], \"unit\": \"N\"}", "dedupe_signature": "46a441a72d6c3d959638274aaee66c4be2f35a56b1e8624de54a5cdc8be2e9db", "difficulty": "medium", "final_answer": {"answer": [-177.7189, 165.7256], "unit": "N"}, "id": "vector_components_005143_243_137", "license": "Apache-2.0", "prompt": "A vector has magnitude 243 N at 137 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=137 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 137, "magnitude": 243.0}, "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. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24.5^2 and multiply by 0.5 * 24.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7218.0063, \"unit\": \"J\"}", "dedupe_signature": "8071b259f07d6d51e899dc942dc64067fbbd3470dc56e9181c848485b3c92336", "difficulty": "easy", "final_answer": {"answer": 7218.0063, "unit": "J"}, "id": "ke_005149_24.05_24.5", "license": "Apache-2.0", "prompt": "A body of mass 24.05 kg moves at 24.5 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 = 24.5^2 and multiply by 0.5 * 24.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.05, "velocity": 24.5}, "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) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 1.3113, \"unit\": \"state_units\"}", "dedupe_signature": "b8f3a51df16d90ad3870793f4efd0b641f54af82cdb22da5bd8fd05c513908f9", "difficulty": "medium", "final_answer": {"answer": 1.3113, "unit": "state_units"}, "id": "euler_decay_005157_48.5_0.41_1.45_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=48.5, 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) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 48.5, "rate": 0.41, "step": 1.45, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [0.668, 1.17, 0.452], \"unit\": \"temperature_units\"}", "dedupe_signature": "abb0a54b0704e2825875e1d8a989a0f293b62c412ace7e3fbf51a749de208d8d", "difficulty": "hard", "final_answer": {"answer": [0.668, 1.17, 0.452], "unit": "temperature_units"}, "id": "heat_step_005159_0.32_0.8_1.1_0.05_2.5_-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=0.8, right=-1.45; current interior values are [1.1, 0.05, 2.5]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [1.1, 0.05, 2.5], "left": 0.8, "r": 0.32, "right": -1.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.2128, \"unit\": \"state_units\"}", "dedupe_signature": "5aaeb72bbc878b1edf459f1f30e66d71e4c14b5248510adde85e1f1549f18f53", "difficulty": "medium", "final_answer": {"answer": 0.2128, "unit": "state_units"}, "id": "euler_decay_005193_16.5_0.51_1.3_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.51 y with y(0)=16.5, 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) = -0.51 y, so each step multiplies y by 1 - h*0.51.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 16.5, "rate": 0.51, "step": 1.3, "steps": 4}, "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": "36b94a8751f3556f2e142849fc745728173b492c3b28bb44c9a60ea2c0a996ba", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005199_consistent_4153435f_396990", "license": "Apache-2.0", "prompt": "In field worksheet case 396990, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.7 kg and a = 8.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 166.635, \"unit\": \"N\"}", "dedupe_signature": "5190e0f5e53e87e0760e2151e89c7cf5a8d855323b16236de54a986141852518", "difficulty": "easy", "final_answer": {"answer": 166.635, "unit": "N"}, "id": "force_005202_20.7_8.05", "license": "Apache-2.0", "prompt": "A cart has mass 20.7 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 = 20.7 kg and a = 8.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.05, "mass": 20.7}, "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=0.28 and add it to the current value.\nFinal: {\"answer\": [0.248, 1.202, 2.27], \"unit\": \"temperature_units\"}", "dedupe_signature": "7e0535d6c38fe0a6af98da061bfad469fdf28ebdd169512f68de9a81bd4bace9", "difficulty": "hard", "final_answer": {"answer": [0.248, 1.202, 2.27], "unit": "temperature_units"}, "id": "heat_step_005213_0.28_1.6_-1.95_2.35_2.55_1.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.6, right=1.75; current interior values are [-1.95, 2.35, 2.55]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.95, 2.35, 2.55], "left": 1.6, "r": 0.28, "right": 1.75}, "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 = 3.87 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 387.3367, \"unit\": \"g\"}", "dedupe_signature": "83c890071a1993b458c6048796f22e90a031caef29b4dc5f7cba6271774a2185", "difficulty": "medium", "final_answer": {"answer": 387.3367, "unit": "g"}, "id": "stoich_mass_005227_calcium_carbonate_3.87", "license": "Apache-2.0", "prompt": "A sample contains 3.87 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.87 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.87}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.5)=11.8 and f(4.5)=-37.2.\n3. The interval width is 7.\nFinal: {\"answer\": -88.9, \"unit\": \"area_units\"}", "dedupe_signature": "7cd41ae20d48dd1ed19585a45b637058fa00738b59ae27eb6a9c109534adccd2", "difficulty": "medium", "final_answer": {"answer": -88.9, "unit": "area_units"}, "id": "trapz_linear_005230_-7_-5.7_-2.5_4.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7x+-5.7 from x=-2.5 to x=4.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.5)=11.8 and f(4.5)=-37.2.\nThe interval width is 7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -5.7, "slope": -7.0, "x0": -2.5, "x1": 4.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=153 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-15.5926, 7.9448], \"unit\": \"N\"}", "dedupe_signature": "fc153daef4562e62167a8317b01ca855ef192bdfd87ff72ba6958fbc37b668ed", "difficulty": "medium", "final_answer": {"answer": [-15.5926, 7.9448], "unit": "N"}, "id": "vector_components_005233_17.5_153", "license": "Apache-2.0", "prompt": "A vector has magnitude 17.5 N at 153 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=153 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 153, "magnitude": 17.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_005236(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_005236\"}", "dedupe_signature": "98aaecd8744fc6ce2fd0a134797425d5a98568b3d94dd9c314cf241c41e7e904", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_005236"}, "id": "code_005236_unit_vector_005236", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_005236(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": "test", "task_family": "python_code_generation", "variables": {"function": "unit_vector_005236"}, "verifier": {"function": "unit_vector_005236", "tests": ["ux, uy = unit_vector_005236(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_005236(0, 5) == (0, 1)", "try:\n    unit_vector_005236(0, 0)\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(-1.1)=-20.41 and f(6.5)=3.15.\n3. The interval width is 7.6.\nFinal: {\"answer\": -65.588, \"unit\": \"area_units\"}", "dedupe_signature": "d03dd503d5f2f91786ee212ab0f54d14322fa70cd3fba606ea9b98d7079896de", "difficulty": "medium", "final_answer": {"answer": -65.588, "unit": "area_units"}, "id": "trapz_linear_005266_3.1_-17_-1.1_6.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.1x+-17 from x=-1.1 to x=6.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.1)=-20.41 and f(6.5)=3.15.\nThe interval width is 7.6.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -17.0, "slope": 3.1, "x0": -1.1, "x1": 6.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.4 kg and a = 7.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 48.96, \"unit\": \"N\"}", "dedupe_signature": "2cbf4850f3c47d0a1b65eaddadf7995e3904fbf110965662137493d3b69cea6d", "difficulty": "easy", "final_answer": {"answer": 48.96, "unit": "N"}, "id": "force_005274_6.4_7.65", "license": "Apache-2.0", "prompt": "A cart has mass 6.4 kg and measured acceleration 7.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.4 kg and a = 7.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.65, "mass": 6.4}, "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 60 mL to 0.06 L.\n3. Compute M = 2.125 / 0.06.\nFinal: {\"answer\": 35.4167, \"unit\": \"mol/L\"}", "dedupe_signature": "636c047e835542e364d2cc5656c77aa829e6b9bd54771ffe6032de7c9250d80f", "difficulty": "medium", "final_answer": {"answer": 35.4167, "unit": "mol/L"}, "id": "molarity_005282_2.125_60", "license": "Apache-2.0", "prompt": "A solution contains 2.125 mol of solute in 60 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 60 mL to 0.06 L.\nCompute M = 2.125 / 0.06.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.125, "volume_ml": 60}, "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: 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": "c555a92d2cc710c82f42c51a926477a81c42ef96725bca72a69d29201d71492e", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005309_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 2843 items and budget 37655, 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": "test", "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. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3490 mL to 3.49 L.\n3. Compute M = 1.34 / 3.49.\nFinal: {\"answer\": 0.384, \"unit\": \"mol/L\"}", "dedupe_signature": "6fc92d23376cf32e60ed7e8edc615d791afc2c52cac2094e8e9d1656c6075285", "difficulty": "medium", "final_answer": {"answer": 0.384, "unit": "mol/L"}, "id": "molarity_005318_1.34_3490", "license": "Apache-2.0", "prompt": "A solution contains 1.34 mol of solute in 3490 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3490 mL to 3.49 L.\nCompute M = 1.34 / 3.49.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.34, "volume_ml": 3490}, "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\": [0.918, 0.678, 0.512], \"unit\": \"temperature_units\"}", "dedupe_signature": "f4d417c21231de61073e656d3d44ed8048370f07f08f90a2ef6e3bd89dc0b8ba", "difficulty": "hard", "final_answer": {"answer": [0.918, 0.678, 0.512], "unit": "temperature_units"}, "id": "heat_step_005321_0.28_0.1_2.5_-0.75_1.1_0.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=0.85; current interior values are [2.5, -0.75, 1.1]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [2.5, -0.75, 1.1], "left": 0.1, "r": 0.28, "right": 0.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 238.0 + 273.15.\nFinal: {\"answer\": 511.15, \"unit\": \"K\"}", "dedupe_signature": "dd84b07f17b1baec812a3b15bfcfdc11f2bcf76b95eaafa663f531e897f8383e", "difficulty": "easy", "final_answer": {"answer": 511.15, "unit": "K"}, "id": "unit_convert_005322_c_to_k_238", "license": "Apache-2.0", "prompt": "Convert 238 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 238.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 238.0}, "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 running_total_005326(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_005326\"}", "dedupe_signature": "fbdcd526a67018435f3cab255713ecb2ae059e3d71af33208e12cafc775d4592", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_005326"}, "id": "code_005326_running_total_005326", "license": "Apache-2.0", "prompt": "Write a Python function running_total_005326(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": "test", "task_family": "python_code_generation", "variables": {"function": "running_total_005326"}, "verifier": {"function": "running_total_005326", "tests": ["assert running_total_005326([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_005326(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_005326([]) == []"], "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=233.5 V and R=178 ohm.\nFinal: {\"answer\": 306.3048, \"unit\": \"W\"}", "dedupe_signature": "94871bb0267effd392fd055c47fb952ae7a11663b346fa8b8fc3262f8bf5ba91", "difficulty": "easy", "final_answer": {"answer": 306.3048, "unit": "W"}, "id": "ohm_power_005333_233.5_178", "license": "Apache-2.0", "prompt": "A resistor has resistance 178 ohm and voltage 233.5 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=233.5 V and R=178 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 178.0, "voltage": 233.5}, "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\ndef normalize_005344(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_005344\"}", "dedupe_signature": "43ff8d39dc03d84f5dbe89108d6f5e0962630c4ce1e98270ab31d44038bde7c1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_005344"}, "id": "code_005344_normalize_005344", "license": "Apache-2.0", "prompt": "Write a Python function normalize_005344(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": "test", "task_family": "python_code_generation", "variables": {"function": "normalize_005344"}, "verifier": {"function": "normalize_005344", "tests": ["out = normalize_005344([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_005344([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_005344([1, 1]) == [0.5, 0.5]", "try:\n    normalize_005344([1, -1])\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=151.1 V and R=107.2 ohm.\nFinal: {\"answer\": 212.9777, \"unit\": \"W\"}", "dedupe_signature": "e6bdb57b351a61356abebddae741b17934edcdb94a281187acf1896e7af57e4e", "difficulty": "easy", "final_answer": {"answer": 212.9777, "unit": "W"}, "id": "ohm_power_005369_151.1_107.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 107.2 ohm and voltage 151.1 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=151.1 V and R=107.2 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 107.2, "voltage": 151.1}, "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 34718.0 / 1000.\nFinal: {\"answer\": 34.718, \"unit\": \"kg\"}", "dedupe_signature": "0ef77870ba9b5cdf8c9a4b38aa2095592e0b6a7064919bc2d42904e726d062d4", "difficulty": "easy", "final_answer": {"answer": 34.718, "unit": "kg"}, "id": "unit_convert_005376_g_to_kg_34718", "license": "Apache-2.0", "prompt": "Convert 34718 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 34718.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 34718.0}, "verifier": {"formula": "value / 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: 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": "9903e76c509506c0e64073be2c2de68d9b885beed38a0857bc217e2551302919", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005381_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 1257 items and budget 66105, 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": "test", "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 Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1140 * 1.175 * 35.\nFinal: {\"answer\": 46882.5, \"unit\": \"J\"}", "dedupe_signature": "85f3422f839e0bd77d9afd58415e2f4a28f9705cdc9a3290df561880a14aaf23", "difficulty": "easy", "final_answer": {"answer": 46882.5, "unit": "J"}, "id": "heat_q_005404_1140_1.175_35", "license": "Apache-2.0", "prompt": "A 1140 g sample has specific heat 1.175 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 = 1140 * 1.175 * 35.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 35, "heat_capacity": 1.175, "mass_g": 1140}, "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 pairwise_ratios_005416(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_005416\"}", "dedupe_signature": "60bb6b600670f122a272d9b2a178693f1d136d5c26ccb093462512aaf95f2349", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_005416"}, "id": "code_005416_pairwise_ratios_005416", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_005416(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": "test", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_005416"}, "verifier": {"function": "pairwise_ratios_005416", "tests": ["assert pairwise_ratios_005416([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_005416([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_005416([1, 2], [1])\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 = 1180 * 2.865 * 2.\nFinal: {\"answer\": 6761.4, \"unit\": \"J\"}", "dedupe_signature": "d350fb2a58d3526fba394414993ef0b3ad8d4adf3fb7d170007d201ef886532c", "difficulty": "easy", "final_answer": {"answer": 6761.4, "unit": "J"}, "id": "heat_q_005440_1180_2.865_2", "license": "Apache-2.0", "prompt": "A 1180 g sample has specific heat 2.865 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 = 1180 * 2.865 * 2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 2, "heat_capacity": 2.865, "mass_g": 1180}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "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 4925.0 / 100.\nFinal: {\"answer\": 49.25, \"unit\": \"m\"}", "dedupe_signature": "ec601590d5f873134aedee77d09961e445845e898c6f76fb79dcdc1ac2650ac9", "difficulty": "easy", "final_answer": {"answer": 49.25, "unit": "m"}, "id": "unit_convert_005448_cm_to_m_4925", "license": "Apache-2.0", "prompt": "Convert 4925 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 4925.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 4925.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=251 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-27.9989, -81.3146], \"unit\": \"N\"}", "dedupe_signature": "5b7ce2984eb4dff8078e844c7bc5a5189b1c153c137066e72461842536b41991", "difficulty": "medium", "final_answer": {"answer": [-27.9989, -81.3146], "unit": "N"}, "id": "vector_components_005467_86_251", "license": "Apache-2.0", "prompt": "A vector has magnitude 86 N at 251 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=251 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 251, "magnitude": 86.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.3, 15.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "1a6f02380fda87d7c75ecc49c0b15b9fa7d10210af3eec06129dd58d3818069c", "difficulty": "medium", "final_answer": {"answer": [1.3, 15.5], "unit": "dimensionless"}, "id": "line_two_point_005468_-17.5_-5.5_1.3_15.5", "license": "Apache-2.0", "prompt": "A line passes through points (-17.5, -7.25) and (-5.5, 8.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -17.5, "x2": -5.5, "y1": -7.25, "y2": 8.35}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 39^2 and multiply by 0.5 * 26.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 20457.45, \"unit\": \"J\"}", "dedupe_signature": "8cde5543d70a8594f252da127b622c6d30f8e1208a70fd24b0c9e5ead7b49485", "difficulty": "easy", "final_answer": {"answer": 20457.45, "unit": "J"}, "id": "ke_005473_26.9_39", "license": "Apache-2.0", "prompt": "A body of mass 26.9 kg moves at 39 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 39^2 and multiply by 0.5 * 26.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.9, "velocity": 39.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=94.5 V and R=49.3 ohm.\nFinal: {\"answer\": 181.141, \"unit\": \"W\"}", "dedupe_signature": "fc9f04a62ece503c1ba7939872691e0d34167923602215ebe8ff5fa8880c328e", "difficulty": "easy", "final_answer": {"answer": 181.141, "unit": "W"}, "id": "ohm_power_005477_94.5_49.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 49.3 ohm and voltage 94.5 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=94.5 V and R=49.3 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 49.3, "voltage": 94.5}, "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. 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": "32cdd0e69be45d2663df70f9931ef9d1dfef2227f4102eb6228a4d7e678c4d29", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005487_consistent_4153435f_817496", "license": "Apache-2.0", "prompt": "In sensor calibration case 817496, 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": "test", "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) = -0.09 y, so each step multiplies y by 1 - h*0.09.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 54.4543, \"unit\": \"state_units\"}", "dedupe_signature": "df39052ec3b5a9e60d59e27804567164a1458f69f2fce9fc5d6a7a23668c92bd", "difficulty": "medium", "final_answer": {"answer": 54.4543, "unit": "state_units"}, "id": "euler_decay_005499_79_0.09_0.45_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=79, step size h=0.45, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 79.0, "rate": 0.09, "step": 0.45, "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=254 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-120.867, -421.5133], \"unit\": \"N\"}", "dedupe_signature": "09a0cbd9376cef99696d97d4423de444a47ad46d85de18cc53902f0c4db70462", "difficulty": "medium", "final_answer": {"answer": [-120.867, -421.5133], "unit": "N"}, "id": "vector_components_005503_438.5_254", "license": "Apache-2.0", "prompt": "A vector has magnitude 438.5 N at 254 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=254 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 254, "magnitude": 438.5}, "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. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.455, -0.111, -0.847], \"unit\": \"temperature_units\"}", "dedupe_signature": "26a303aca0e62e54118bcc5df73dddd2b8228c9104284426150b8d7e89f40a20", "difficulty": "hard", "final_answer": {"answer": [0.455, -0.111, -0.847], "unit": "temperature_units"}, "id": "heat_step_005519_0.26_1.8_-0.65_1.15_-1.9_-0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.8, right=-0.9; current interior values are [-0.65, 1.15, -1.9]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, 1.15, -1.9], "left": 1.8, "r": 0.26, "right": -0.9}, "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=357 mg, t=306.5 h, and T_half=67 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 14.9819, \"unit\": \"mg\"}", "dedupe_signature": "74769939e0f3f8555beeb14b5fd596da7b92c7fc1cb77ae12f6bb07b21d4e3c3", "difficulty": "medium", "final_answer": {"answer": 14.9819, "unit": "mg"}, "id": "half_life_005532_357_67_306.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 357 mg. Its half-life is 67 hours. How many mg remain after 306.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=357 mg, t=306.5 h, and T_half=67 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 306.5, "half_life": 67.0, "initial_amount": 357.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.38 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 236.7738, \"unit\": \"g\"}", "dedupe_signature": "7d9b130a25703c9d515c6f6a50f8474424d0331b3c5634c47a5fe22e2462338f", "difficulty": "medium", "final_answer": {"answer": 236.7738, "unit": "g"}, "id": "stoich_mass_005533_carbon_dioxide_5.38", "license": "Apache-2.0", "prompt": "A sample contains 5.38 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.38 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.38}, "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\": [-1.1, -14.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "923b337ee88ff8cf6fae05b1979a609d7dc9f89dc3752efffadcbc389cade032", "difficulty": "medium", "final_answer": {"answer": [-1.1, -14.0], "unit": "dimensionless"}, "id": "line_two_point_005540_13.5_15.5_-1.1_-14", "license": "Apache-2.0", "prompt": "A line passes through points (13.5, -28.85) and (15.5, -31.05). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 13.5, "x2": 15.5, "y1": -28.85, "y2": -31.05}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 810 * 1.845 * 23.\nFinal: {\"answer\": 34372.35, \"unit\": \"J\"}", "dedupe_signature": "b198cb90f2792c4ccaf867c05716cc1a29a67cf4cbc3fb4c501d2759afcdedec", "difficulty": "easy", "final_answer": {"answer": 34372.35, "unit": "J"}, "id": "heat_q_005548_810_1.845_23", "license": "Apache-2.0", "prompt": "A 810 g sample has specific heat 1.845 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 = 810 * 1.845 * 23.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 23, "heat_capacity": 1.845, "mass_g": 810}, "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) = -0.25 y, so each step multiplies y by 1 - h*0.25.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.3466, \"unit\": \"state_units\"}", "dedupe_signature": "af0d79724d450e167d4c991f69e5165506f14ee62ffad3f520a45c759eaa0c16", "difficulty": "medium", "final_answer": {"answer": 0.3466, "unit": "state_units"}, "id": "euler_decay_005553_17.5_0.25_1.55_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.25 y with y(0)=17.5, step size h=1.55, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.25 y, so each step multiplies y by 1 - h*0.25.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 17.5, "rate": 0.25, "step": 1.55, "steps": 8}, "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 = 1510 * 3.955 * 32.\nFinal: {\"answer\": 191105.6, \"unit\": \"J\"}", "dedupe_signature": "2510e18f9aa3aec3680ed3f0ded1090adae0111508d7369edc19c2c0ab12d2b8", "difficulty": "easy", "final_answer": {"answer": 191105.6, "unit": "J"}, "id": "heat_q_005566_1510_3.955_32", "license": "Apache-2.0", "prompt": "A 1510 g sample has specific heat 3.955 J/(g*K). How much heat is needed to raise its temperature by 32 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1510 * 3.955 * 32.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 32, "heat_capacity": 3.955, "mass_g": 1510}, "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=509.5 mg, t=105.5 h, and T_half=41.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 87.4732, \"unit\": \"mg\"}", "dedupe_signature": "bde1e659294ea45b08a0c034425507d96391c9a1fed9e7d80e96a882449e2140", "difficulty": "medium", "final_answer": {"answer": 87.4732, "unit": "mg"}, "id": "half_life_005568_509.5_41.5_105.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 509.5 mg. Its half-life is 41.5 hours. How many mg remain after 105.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=509.5 mg, t=105.5 h, and T_half=41.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 105.5, "half_life": 41.5, "initial_amount": 509.5}, "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 = 1.28 * 8.314 * 464 / 21.9.\nFinal: {\"answer\": 225.4726, \"unit\": \"kPa\"}", "dedupe_signature": "1f1b87277fdd89840e547c52da5befd9737b6c4c533991121f5d96bccdea391a", "difficulty": "medium", "final_answer": {"answer": 225.4726, "unit": "kPa"}, "id": "ideal_gas_005619_1.28_464_21.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.28 mol, T=464 K, and V=21.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.28 * 8.314 * 464 / 21.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.28, "temp_k": 464, "volume_l": 21.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=9 degrees through the sine of 2 theta.\n3. Substitute v=35.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 39.2521, \"unit\": \"m\"}", "dedupe_signature": "e19a4301afe495f4d6d4e983bc7d3336abaec5c2cd3db9ce2e55fadea8b9c20f", "difficulty": "medium", "final_answer": {"answer": 39.2521, "unit": "m"}, "id": "projectile_range_005636_35.3_9", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 35.3 m/s and angle 9 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=9 degrees through the sine of 2 theta.\nSubstitute v=35.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 9, "gravity": 9.81, "speed": 35.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_005650(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_005650\"}", "dedupe_signature": "d7fc6c36d9cbee1b3dc318812ba1a2a47b10757ff63a98413d2b83b1d7e3a5a8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_005650"}, "id": "code_005650_weighted_sum_005650", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_005650(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": "test", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_005650"}, "verifier": {"function": "weighted_sum_005650", "tests": ["assert weighted_sum_005650([2, 3], [4, 5]) == 23", "assert weighted_sum_005650([], []) == 0", "try:\n    weighted_sum_005650([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.85^2 and multiply by 0.5 * 5.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2036.6061, \"unit\": \"J\"}", "dedupe_signature": "d6604379e946b538fdfb22fb4e8434056cf29a979a3d23820b0c728f734116b9", "difficulty": "easy", "final_answer": {"answer": 2036.6061, "unit": "J"}, "id": "ke_005653_5.65_26.85", "license": "Apache-2.0", "prompt": "A body of mass 5.65 kg moves at 26.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.85^2 and multiply by 0.5 * 5.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.65, "velocity": 26.85}, "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(4.6)=45.28 and f(8.5)=67.9.\n3. The interval width is 3.9.\nFinal: {\"answer\": 220.701, \"unit\": \"area_units\"}", "dedupe_signature": "4ef0777f1e104f1fe9b0d113d2602bb8aa069cea806541f1cf3318e20563f6ee", "difficulty": "medium", "final_answer": {"answer": 220.701, "unit": "area_units"}, "id": "trapz_linear_005662_5.8_18.6_4.6_8.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.8x+18.6 from x=4.6 to x=8.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.6)=45.28 and f(8.5)=67.9.\nThe interval width is 3.9.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 18.6, "slope": 5.8, "x0": 4.6, "x1": 8.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=77 degrees and keep the unit as newtons.\nFinal: {\"answer\": [105.1646, 455.518], \"unit\": \"N\"}", "dedupe_signature": "2b94f021d7b9c17b56b937ecce942013bcfb4ced30d05ce37f021147ca7e655c", "difficulty": "medium", "final_answer": {"answer": [105.1646, 455.518], "unit": "N"}, "id": "vector_components_005665_467.5_77", "license": "Apache-2.0", "prompt": "A vector has magnitude 467.5 N at 77 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=77 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 77, "magnitude": 467.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.8, -2.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "e68c0b22455b5576cb41ae8a3f22984bbcbe630d975c76b998110369d294daf2", "difficulty": "medium", "final_answer": {"answer": [6.8, -2.25], "unit": "dimensionless"}, "id": "line_two_point_005666_-3.25_-2.5_6.8_-2.25", "license": "Apache-2.0", "prompt": "A line passes through points (-3.25, -24.35) and (-2.5, -19.25). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -3.25, "x2": -2.5, "y1": -24.349999999999998, "y2": -19.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.34 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 58.9734, \"unit\": \"g\"}", "dedupe_signature": "bec0df58175b5bb1f5e83a4173f67e5a25a41c9f2aa1d6714ea42fb3e5162b9f", "difficulty": "medium", "final_answer": {"answer": 58.9734, "unit": "g"}, "id": "stoich_mass_005677_carbon_dioxide_1.34", "license": "Apache-2.0", "prompt": "A sample contains 1.34 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 = 1.34 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.34}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1805 mL to 1.805 L.\n3. Compute M = 2.165 / 1.805.\nFinal: {\"answer\": 1.1994, \"unit\": \"mol/L\"}", "dedupe_signature": "853d82eb9fb6da03bbde8014fa79dca7771bc1e1e56fa56002c6154d67c1abac", "difficulty": "medium", "final_answer": {"answer": 1.1994, "unit": "mol/L"}, "id": "molarity_005678_2.165_1805", "license": "Apache-2.0", "prompt": "A solution contains 2.165 mol of solute in 1805 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1805 mL to 1.805 L.\nCompute M = 2.165 / 1.805.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.165, "volume_ml": 1805}, "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=335 degrees and keep the unit as newtons.\nFinal: {\"answer\": [372.0393, -173.4848], \"unit\": \"N\"}", "dedupe_signature": "fdccd1429575067763ce9d74ecdd4e03e32af06f253e03425e6b5635a015df30", "difficulty": "medium", "final_answer": {"answer": [372.0393, -173.4848], "unit": "N"}, "id": "vector_components_005683_410.5_335", "license": "Apache-2.0", "prompt": "A vector has magnitude 410.5 N at 335 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=335 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 335, "magnitude": 410.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.85, -8.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "9c1a7cf633b4408712f384dfe8a43829ab0c5fb97a2752251583b0f8c1da7c7a", "difficulty": "medium", "final_answer": {"answer": [-8.85, -8.75], "unit": "dimensionless"}, "id": "line_two_point_005684_1.5_6.5_-8.85_-8.75", "license": "Apache-2.0", "prompt": "A line passes through points (1.5, -22.025) and (6.5, -66.275). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 1.5, "x2": 6.5, "y1": -22.025, "y2": -66.275}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=83 degrees through the sine of 2 theta.\n3. Substitute v=26.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 17.8448, \"unit\": \"m\"}", "dedupe_signature": "07ba37dc8c354a47e8391b71914327c353e0bc9a8cb0d3a49c07a1eeb707b2a6", "difficulty": "medium", "final_answer": {"answer": 17.8448, "unit": "m"}, "id": "projectile_range_005690_26.9_83", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 26.9 m/s and angle 83 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=83 degrees through the sine of 2 theta.\nSubstitute v=26.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 83, "gravity": 9.81, "speed": 26.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1838.5 / 100.\nFinal: {\"answer\": 18.385, \"unit\": \"m\"}", "dedupe_signature": "0b52331a7568bf46b892bb41e0a027cdf9a1b805bc414ea8d2bc502ff6c9be37", "difficulty": "easy", "final_answer": {"answer": 18.385, "unit": "m"}, "id": "unit_convert_005700_cm_to_m_1838.5", "license": "Apache-2.0", "prompt": "Convert 1838.5 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 1838.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 1838.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3630 mL to 3.63 L.\n3. Compute M = 2.655 / 3.63.\nFinal: {\"answer\": 0.7314, \"unit\": \"mol/L\"}", "dedupe_signature": "83f16a7119b627b79433b02e117409df406d0e9ece07433b482cb685c29c5e17", "difficulty": "medium", "final_answer": {"answer": 0.7314, "unit": "mol/L"}, "id": "molarity_005714_2.655_3630", "license": "Apache-2.0", "prompt": "A solution contains 2.655 mol of solute in 3630 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3630 mL to 3.63 L.\nCompute M = 2.655 / 3.63.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.655, "volume_ml": 3630}, "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=366.5 mg, t=105 h, and T_half=78 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 144.1588, \"unit\": \"mg\"}", "dedupe_signature": "0bb4731e41d42288f141bdfa858e577470eaba61cf9a83ba56fea3b313ad95bf", "difficulty": "medium", "final_answer": {"answer": 144.1588, "unit": "mg"}, "id": "half_life_005730_366.5_78_105", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 366.5 mg. Its half-life is 78 hours. How many mg remain after 105 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=366.5 mg, t=105 h, and T_half=78 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 105.0, "half_life": 78.0, "initial_amount": 366.5}, "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=0.28 and add it to the current value.\nFinal: {\"answer\": [-1.544, -0.376, 1.27], \"unit\": \"temperature_units\"}", "dedupe_signature": "f5cd7ea8f0eb01731a51c12a307bd8503fe3f37a2045e9dc81395ddf70c82811", "difficulty": "hard", "final_answer": {"answer": [-1.544, -0.376, 1.27], "unit": "temperature_units"}, "id": "heat_step_005735_0.28_-1.85_-1.95_-0.6_1.55_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=-1.85, right=2.7; current interior values are [-1.95, -0.6, 1.55]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.95, -0.6, 1.55], "left": -1.85, "r": 0.28, "right": 2.7}, "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: 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": "cf9dec6df7a95f49ef83d653a4875e65a360c3e9f24df603932a937351ec2a9e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005741_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [1.45, -0.45, 2.3], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "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. Keep the boundary values fixed and update only the three interior grid points.\n2. 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\": [0.009, -0.14, 0.719], \"unit\": \"temperature_units\"}", "dedupe_signature": "4559056156f75cd4d9889758eb4d3a89f9b9c358f8629c5221adf05724054a58", "difficulty": "hard", "final_answer": {"answer": [0.009, -0.14, 0.719], "unit": "temperature_units"}, "id": "heat_step_005753_0.34_1.95_-0.45_-1.5_1.45_2.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=2.25; current interior values are [-0.45, -1.5, 1.45]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.45, -1.5, 1.45], "left": 1.95, "r": 0.34, "right": 2.25}, "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=111.5 V and R=161.4 ohm.\nFinal: {\"answer\": 77.0276, \"unit\": \"W\"}", "dedupe_signature": "59ca7f1c4f5987b21d0430eefb983b528f906e8087166a01c69dc438243f988f", "difficulty": "easy", "final_answer": {"answer": 77.0276, "unit": "W"}, "id": "ohm_power_005765_111.5_161.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 161.4 ohm and voltage 111.5 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=111.5 V and R=161.4 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 161.4, "voltage": 111.5}, "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) = -0.62 y, so each step multiplies y by 1 - h*0.62.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 0.3188, \"unit\": \"state_units\"}", "dedupe_signature": "a8ebbac6237ec2a12f5312055ad1407ba1eca5d289266e1362b3c462d12994af", "difficulty": "medium", "final_answer": {"answer": 0.3188, "unit": "state_units"}, "id": "euler_decay_005769_12_0.62_1.35_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.62 y with y(0)=12, step size h=1.35, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 12.0, "rate": 0.62, "step": 1.35, "steps": 2}, "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 normalize_005776(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_005776\"}", "dedupe_signature": "884a32d6834a0d69c279c0f5d3444ed6c5ca79af60638f2adbe53c44d148661a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_005776"}, "id": "code_005776_normalize_005776", "license": "Apache-2.0", "prompt": "Write a Python function normalize_005776(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": "test", "task_family": "python_code_generation", "variables": {"function": "normalize_005776"}, "verifier": {"function": "normalize_005776", "tests": ["out = normalize_005776([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_005776([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_005776([1, 1]) == [0.5, 0.5]", "try:\n    normalize_005776([1, -1])\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 = 4.19 * 8.314 * 300 / 63.3.\nFinal: {\"answer\": 165.0979, \"unit\": \"kPa\"}", "dedupe_signature": "fca664fe29f2b958726b145620cfb781043e96fa60a77fe96a97ef1818977d0e", "difficulty": "medium", "final_answer": {"answer": 165.0979, "unit": "kPa"}, "id": "ideal_gas_005817_4.19_300_63.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.19 mol, T=300 K, and V=63.3 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 = 4.19 * 8.314 * 300 / 63.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 4.19, "temp_k": 300, "volume_l": 63.3}, "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. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "83b294eb61cc4f70be0e74309dc39db7b4fc62a42224b44515fd679a19d5b41a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005829_inconsistent_74ac0b02_541130", "license": "Apache-2.0", "prompt": "In model card equation case 541130, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "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 10952.0 / 1000.\nFinal: {\"answer\": 10.952, \"unit\": \"kg\"}", "dedupe_signature": "d348507912ef63e200214ce22ba62519b7f8c3fe35a8dbb577c857f158f87f9e", "difficulty": "easy", "final_answer": {"answer": 10.952, "unit": "kg"}, "id": "unit_convert_005862_g_to_kg_10952", "license": "Apache-2.0", "prompt": "Convert 10952 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 10952.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 10952.0}, "verifier": {"formula": "value / 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": "9ee4d22449dcffd63c68a6f0cf428c0b3d7681e21952a008a5dee43ac31272e8", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005867_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field clinical record from batch 286382 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": "test", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.85^2 and multiply by 0.5 * 0.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 108.1384, \"unit\": \"J\"}", "dedupe_signature": "e042a58246f5be6db7a85864759baecd2930b31b2c74fb01612afcfbe6c7de9f", "difficulty": "easy", "final_answer": {"answer": 108.1384, "unit": "J"}, "id": "ke_005887_0.3_26.85", "license": "Apache-2.0", "prompt": "A body of mass 0.3 kg moves at 26.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.85^2 and multiply by 0.5 * 0.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.3, "velocity": 26.85}, "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 = 690 * 4.24 * 70.\nFinal: {\"answer\": 204792.0, \"unit\": \"J\"}", "dedupe_signature": "61550b067188a296c9d08b3a621dbd541b00b9b17a48f7569c381ea713235183", "difficulty": "easy", "final_answer": {"answer": 204792.0, "unit": "J"}, "id": "heat_q_005908_690_4.24_70", "license": "Apache-2.0", "prompt": "A 690 g sample has specific heat 4.24 J/(g*K). How much heat is needed to raise its temperature by 70 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 690 * 4.24 * 70.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 70, "heat_capacity": 4.24, "mass_g": 690}, "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 330 mL to 0.33 L.\n3. Compute M = 1.035 / 0.33.\nFinal: {\"answer\": 3.1364, \"unit\": \"mol/L\"}", "dedupe_signature": "8c9bda9aef1b0a656abb92481c553af5f1396920caa4d9acc34e22efe1e6195a", "difficulty": "medium", "final_answer": {"answer": 3.1364, "unit": "mol/L"}, "id": "molarity_005930_1.035_330", "license": "Apache-2.0", "prompt": "A solution contains 1.035 mol of solute in 330 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 330 mL to 0.33 L.\nCompute M = 1.035 / 0.33.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.035, "volume_ml": 330}, "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=5 degrees through the sine of 2 theta.\n3. Substitute v=76.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 103.0505, \"unit\": \"m\"}", "dedupe_signature": "0656f62dfaca87a87c464d01f892d391b1c17500b76a56ce58433673b019d973", "difficulty": "medium", "final_answer": {"answer": 103.0505, "unit": "m"}, "id": "projectile_range_005960_76.3_5", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 76.3 m/s and angle 5 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=5 degrees through the sine of 2 theta.\nSubstitute v=76.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 5, "gravity": 9.81, "speed": 76.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3205 mL to 3.205 L.\n3. Compute M = 3.925 / 3.205.\nFinal: {\"answer\": 1.2246, \"unit\": \"mol/L\"}", "dedupe_signature": "0fd6b1b664f72ccd5f310dfa9435fba4dabc954bf635a59951e252e06b3c7a0b", "difficulty": "medium", "final_answer": {"answer": 1.2246, "unit": "mol/L"}, "id": "molarity_005966_3.925_3205", "license": "Apache-2.0", "prompt": "A solution contains 3.925 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 = 3.925 / 3.205.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 3.925, "volume_ml": 3205}, "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: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "0915c494778acae30d9a5ca357f0b15a025524ee3b4268e8300511f7e779aebb", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005975_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.84 mol and T=504 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.3 kg and a = 12.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 229.665, \"unit\": \"N\"}", "dedupe_signature": "3b7ea7902490d3f7ca73c8dd0f1b75b49389ed7af569627b24753e25057a0015", "difficulty": "easy", "final_answer": {"answer": 229.665, "unit": "N"}, "id": "force_005976_18.3_12.55", "license": "Apache-2.0", "prompt": "A cart has mass 18.3 kg and measured acceleration 12.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.3 kg and a = 12.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.55, "mass": 18.3}, "verifier": {"formula": "mass * acceleration", "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 211.0 / 100.\nFinal: {\"answer\": 2.11, \"unit\": \"m\"}", "dedupe_signature": "302a7c32947ba4eb0e59c8daa81cb48297d6d53e848a539149c7240344ddfe4a", "difficulty": "easy", "final_answer": {"answer": 2.11, "unit": "m"}, "id": "unit_convert_005988_cm_to_m_211", "license": "Apache-2.0", "prompt": "Convert 211 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 211.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 211.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. 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": "a7723b3eb9f837adf5568d59fa8a68a6566d282dd605bed164118e96a5bbd92d", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005991_inconsistent_56040f5d_534652", "license": "Apache-2.0", "prompt": "In quality-control check case 534652, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "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=54 degrees through the sine of 2 theta.\n3. Substitute v=51.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 261.1392, \"unit\": \"m\"}", "dedupe_signature": "1eb4199c6cacd3bbd870fe28eea8740df874cecaa37ae4985129319cd72e38d4", "difficulty": "medium", "final_answer": {"answer": 261.1392, "unit": "m"}, "id": "projectile_range_005996_51.9_54", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 51.9 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=54 degrees through the sine of 2 theta.\nSubstitute v=51.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 54, "gravity": 9.81, "speed": 51.9}, "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 = 1670 * 3.855 * 21.\nFinal: {\"answer\": 135194.85, \"unit\": \"J\"}", "dedupe_signature": "9f0dd1ac999b8e7f7456c5dc0d89a1b3f14f6d613df4dc67eaf523cc7e384a8a", "difficulty": "easy", "final_answer": {"answer": 135194.85, "unit": "J"}, "id": "heat_q_005998_1670_3.855_21", "license": "Apache-2.0", "prompt": "A 1670 g sample has specific heat 3.855 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 = 1670 * 3.855 * 21.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 3.855, "mass_g": 1670}, "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 = 14^2 and multiply by 0.5 * 8.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 867.3, \"unit\": \"J\"}", "dedupe_signature": "4342a780a0045157cb421d0196c5630580b1915ceab4f2d25cada6134094aa84", "difficulty": "easy", "final_answer": {"answer": 867.3, "unit": "J"}, "id": "ke_006013_8.85_14", "license": "Apache-2.0", "prompt": "A body of mass 8.85 kg moves at 14 m/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 and multiply by 0.5 * 8.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.85, "velocity": 14.0}, "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 = 1.48 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 26.6622, \"unit\": \"g\"}", "dedupe_signature": "ac01fa37fabccdde5e2cc3c380e2696cf4529b09af9c0f8006493a6daa5f003a", "difficulty": "medium", "final_answer": {"answer": 26.6622, "unit": "g"}, "id": "stoich_mass_006019_water_1.48", "license": "Apache-2.0", "prompt": "A sample contains 1.48 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.48 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.48}, "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(4.5)=-35.5 and f(13.9)=-106.94.\n3. The interval width is 9.4.\nFinal: {\"answer\": -669.468, \"unit\": \"area_units\"}", "dedupe_signature": "f37fd0ba398df9a0a37d4ec7742ffd98fec924b5ba104b389993814eb3785624", "difficulty": "medium", "final_answer": {"answer": -669.468, "unit": "area_units"}, "id": "trapz_linear_006022_-7.6_-1.3_4.5_13.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.6x+-1.3 from x=4.5 to x=13.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.5)=-35.5 and f(13.9)=-106.94.\nThe interval width is 9.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -1.3, "slope": -7.6, "x0": 4.5, "x1": 13.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "5051d7bf093d77acca0ab897681288fa345c72e5130bc7faf996a4f161110a0c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_006029_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.98 mol and T=285 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"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": "467b0c08a3e31adb2d229892ef5d69e62c66b4c7b844e2048542974172a01ff9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006045_inconsistent_74ac0b02_176354", "license": "Apache-2.0", "prompt": "In model card equation case 176354, 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": "test", "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 = 1300 * 4.365 * 68.\nFinal: {\"answer\": 385866.0, \"unit\": \"J\"}", "dedupe_signature": "9c774f970b189ce6728d22f976855ae3f08ab5494b8148f776830cf4fb81b8ce", "difficulty": "easy", "final_answer": {"answer": 385866.0, "unit": "J"}, "id": "heat_q_006052_1300_4.365_68", "license": "Apache-2.0", "prompt": "A 1300 g sample has specific heat 4.365 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 = 1300 * 4.365 * 68.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 68, "heat_capacity": 4.365, "mass_g": 1300}, "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 = 4.95^2 and multiply by 0.5 * 1.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 20.2146, \"unit\": \"J\"}", "dedupe_signature": "15c94c7c6293e0e51e8c96cfd63d9c3ed5b413b6253d067b56873c2dec24b195", "difficulty": "easy", "final_answer": {"answer": 20.2146, "unit": "J"}, "id": "ke_006067_1.65_4.95", "license": "Apache-2.0", "prompt": "A body of mass 1.65 kg moves at 4.95 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 = 4.95^2 and multiply by 0.5 * 1.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.65, "velocity": 4.95}, "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 760 mL to 0.76 L.\n3. Compute M = 2.805 / 0.76.\nFinal: {\"answer\": 3.6908, \"unit\": \"mol/L\"}", "dedupe_signature": "2a61cdf651b3bf7553fe605f1cfbf9c28a4f9729028d7fa134077142ec49efad", "difficulty": "medium", "final_answer": {"answer": 3.6908, "unit": "mol/L"}, "id": "molarity_006074_2.805_760", "license": "Apache-2.0", "prompt": "A solution contains 2.805 mol of solute in 760 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 760 mL to 0.76 L.\nCompute M = 2.805 / 0.76.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.805, "volume_ml": 760}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 2.5708, \"unit\": \"state_units\"}", "dedupe_signature": "83dc3179cab0b3a7a464c5e87e3631846cbf74cd4a01551b29a5b2a7f96efd9f", "difficulty": "medium", "final_answer": {"answer": 2.5708, "unit": "state_units"}, "id": "euler_decay_006075_69_0.47_0.55_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.47 y with y(0)=69, step size h=0.55, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 69.0, "rate": 0.47, "step": 0.55, "steps": 11}, "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 = 34.15^2 and multiply by 0.5 * 23.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13615.6477, \"unit\": \"J\"}", "dedupe_signature": "cc0355d503caa72c9dd3d687874ba7032f3ee4a28f8148d495e886296ea03d84", "difficulty": "easy", "final_answer": {"answer": 13615.6477, "unit": "J"}, "id": "ke_006085_23.35_34.15", "license": "Apache-2.0", "prompt": "A body of mass 23.35 kg moves at 34.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.15^2 and multiply by 0.5 * 23.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.35, "velocity": 34.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=85 degrees through the sine of 2 theta.\n3. Substitute v=18.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 5.9929, \"unit\": \"m\"}", "dedupe_signature": "b100335866ab9a192bd362568820b98c1d5e4d534a0acf05d66a0e2f3c396eb2", "difficulty": "medium", "final_answer": {"answer": 5.9929, "unit": "m"}, "id": "projectile_range_006086_18.4_85", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 18.4 m/s and angle 85 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=85 degrees through the sine of 2 theta.\nSubstitute v=18.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 85, "gravity": 9.81, "speed": 18.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.82 * 8.314 * 394 / 50.2.\nFinal: {\"answer\": 184.0143, \"unit\": \"kPa\"}", "dedupe_signature": "bd64d3b5910b79f1a51675c44444ac1aea510bfb6a162327208a64a6d2560094", "difficulty": "medium", "final_answer": {"answer": 184.0143, "unit": "kPa"}, "id": "ideal_gas_006087_2.82_394_50.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.82 mol, T=394 K, and V=50.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.82 * 8.314 * 394 / 50.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.82, "temp_k": 394, "volume_l": 50.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1630 * 4.55 * 45.\nFinal: {\"answer\": 333742.5, \"unit\": \"J\"}", "dedupe_signature": "18e521385264e2e69a8b31651843234e79666c527c3bb740f5b703333d9c8ea6", "difficulty": "easy", "final_answer": {"answer": 333742.5, "unit": "J"}, "id": "heat_q_006106_1630_4.55_45", "license": "Apache-2.0", "prompt": "A 1630 g sample has specific heat 4.55 J/(g*K). How much heat is needed to raise its temperature by 45 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1630 * 4.55 * 45.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 45, "heat_capacity": 4.55, "mass_g": 1630}, "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=226 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-92.0422, -95.3125], \"unit\": \"N\"}", "dedupe_signature": "ed1e1ade310dcfef83672dcc3999ba1d02f47844c55303df37ca49470fcbdd97", "difficulty": "medium", "final_answer": {"answer": [-92.0422, -95.3125], "unit": "N"}, "id": "vector_components_006115_132.5_226", "license": "Apache-2.0", "prompt": "A vector has magnitude 132.5 N at 226 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=226 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 226, "magnitude": 132.5}, "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": "97fab20683f37bd6e2b846e7ceccbe843d152ce1b94bc13710ab35af76b4bc7a", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006119_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=37.5 and h=1.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.6 kg and a = 7.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 171.1, \"unit\": \"N\"}", "dedupe_signature": "e5d042630b2fe3a38b66543f64e31dbeed98e475bb9de2d56aea27a7bf58af31", "difficulty": "easy", "final_answer": {"answer": 171.1, "unit": "N"}, "id": "force_006120_23.6_7.25", "license": "Apache-2.0", "prompt": "A cart has mass 23.6 kg and measured acceleration 7.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.6 kg and a = 7.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.25, "mass": 23.6}, "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(-7.8)=-18.38 and f(-3)=-15.5.\n3. The interval width is 4.8.\nFinal: {\"answer\": -81.312, \"unit\": \"area_units\"}", "dedupe_signature": "44507a9f9c7804c11336498f27e5cccde17f86b5d8d9f67cb6ddda28d34c0601", "difficulty": "medium", "final_answer": {"answer": -81.312, "unit": "area_units"}, "id": "trapz_linear_006130_0.6_-13.7_-7.8_-3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+-13.7 from x=-7.8 to x=-3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.8)=-18.38 and f(-3)=-15.5.\nThe interval width is 4.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": -13.7, "slope": 0.6, "x0": -7.8, "x1": -3.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2515 mL to 2.515 L.\n3. Compute M = 4.8 / 2.515.\nFinal: {\"answer\": 1.9085, \"unit\": \"mol/L\"}", "dedupe_signature": "b5ea4de246c0b7673bc5f63177fd79b6312dd861b5bc8df9406690c189103a2b", "difficulty": "medium", "final_answer": {"answer": 1.9085, "unit": "mol/L"}, "id": "molarity_006164_4.8_2515", "license": "Apache-2.0", "prompt": "A solution contains 4.8 mol of solute in 2515 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2515 mL to 2.515 L.\nCompute M = 4.8 / 2.515.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.8, "volume_ml": 2515}, "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 = 1375 * 4.475 * 32.\nFinal: {\"answer\": 196900.0, \"unit\": \"J\"}", "dedupe_signature": "117b02f9c042d7712ea005e408e8a0ab5151a60041639a198a5cd4f98de9cbd0", "difficulty": "easy", "final_answer": {"answer": 196900.0, "unit": "J"}, "id": "heat_q_006178_1375_4.475_32", "license": "Apache-2.0", "prompt": "A 1375 g sample has specific heat 4.475 J/(g*K). How much heat is needed to raise its temperature by 32 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1375 * 4.475 * 32.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 32, "heat_capacity": 4.475, "mass_g": 1375}, "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 = 16.1^2 and multiply by 0.5 * 23.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3104.0398, \"unit\": \"J\"}", "dedupe_signature": "aac27193ee1feb973c67ac9aaa8edfb7d177edbb4925a8ee29b5fc09ff435c36", "difficulty": "easy", "final_answer": {"answer": 3104.0398, "unit": "J"}, "id": "ke_006193_23.95_16.1", "license": "Apache-2.0", "prompt": "A body of mass 23.95 kg moves at 16.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.1^2 and multiply by 0.5 * 23.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.95, "velocity": 16.1}, "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\": [-0.15, 10.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c2c0d8cfc297ba1bf1195e433c45e258244d5de2be64dfc2d74fab60c23b247c", "difficulty": "medium", "final_answer": {"answer": [-0.15, 10.25], "unit": "dimensionless"}, "id": "line_two_point_006206_-15.5_-9.25_-0.15_10.25", "license": "Apache-2.0", "prompt": "A line passes through points (-15.5, 12.575) and (-9.25, 11.6375). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -15.5, "x2": -9.25, "y1": 12.575, "y2": 11.6375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24.55^2 and multiply by 0.5 * 5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1506.7562, \"unit\": \"J\"}", "dedupe_signature": "edfc3084b6ed58e892a19d3abf59a35aee5c244919cad8c1213e0550708e012c", "difficulty": "easy", "final_answer": {"answer": 1506.7562, "unit": "J"}, "id": "ke_006211_5_24.55", "license": "Apache-2.0", "prompt": "A body of mass 5 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 * 5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.0, "velocity": 24.55}, "verifier": {"formula": "0.5 * mass * velocity ** 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: 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": "e50530bab6579441f3dbf07ff1b3d630f9f755a92b866f88be9de2d339621c6e", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006227_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=6.5 and h=1.6, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "test", "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 = 2.33 * 8.314 * 375 / 74.2.\nFinal: {\"answer\": 97.9024, \"unit\": \"kPa\"}", "dedupe_signature": "8b6bb949bba44b9a059053df2ed2d243af01ad4e173c71e67b66c1517be66e9a", "difficulty": "medium", "final_answer": {"answer": 97.9024, "unit": "kPa"}, "id": "ideal_gas_006249_2.33_375_74.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.33 mol, T=375 K, and V=74.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.33 * 8.314 * 375 / 74.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.33, "temp_k": 375, "volume_l": 74.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=75 degrees and keep the unit as newtons.\nFinal: {\"answer\": [16.9526, 63.2681], \"unit\": \"N\"}", "dedupe_signature": "f72e0a7c501c7c62bf7054b34546fcbeca63e9e3546d3b31bfd43e67598693da", "difficulty": "medium", "final_answer": {"answer": [16.9526, 63.2681], "unit": "N"}, "id": "vector_components_006259_65.5_75", "license": "Apache-2.0", "prompt": "A vector has magnitude 65.5 N at 75 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=75 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 75, "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=743 mg, t=250.5 h, and T_half=120 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 174.819, \"unit\": \"mg\"}", "dedupe_signature": "79a005d0c39ff30ee78b4d2374e7bdb84ae2d72be26dafe7052b92340b4620cd", "difficulty": "medium", "final_answer": {"answer": 174.819, "unit": "mg"}, "id": "half_life_006270_743_120_250.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 743 mg. Its half-life is 120 hours. How many mg remain after 250.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=743 mg, t=250.5 h, and T_half=120 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 250.5, "half_life": 120.0, "initial_amount": 743.0}, "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)=76.71 and f(-3.5)=32.05.\n3. The interval width is 5.8.\nFinal: {\"answer\": 315.404, \"unit\": \"area_units\"}", "dedupe_signature": "f2ed514c9ee33fc2d3ec55fcc04d384e07f0ae11803c538d0e43e9bbef850298", "difficulty": "medium", "final_answer": {"answer": 315.404, "unit": "area_units"}, "id": "trapz_linear_006274_-7.7_5.1_-9.3_-3.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+5.1 from x=-9.3 to x=-3.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.3)=76.71 and f(-3.5)=32.05.\nThe interval width is 5.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 5.1, "slope": -7.7, "x0": -9.3, "x1": -3.500000000000001}, "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 weighted_sum_006280(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_006280\"}", "dedupe_signature": "db8384e487de8409bdbb9b4c5e6224dac37b6f59d6e11839de14cae891de08dc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_006280"}, "id": "code_006280_weighted_sum_006280", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_006280(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": "test", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_006280"}, "verifier": {"function": "weighted_sum_006280", "tests": ["assert weighted_sum_006280([2, 3], [4, 5]) == 23", "assert weighted_sum_006280([], []) == 0", "try:\n    weighted_sum_006280([1], [1, 2])\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=154.2 V and R=62.5 ohm.\nFinal: {\"answer\": 380.4422, \"unit\": \"W\"}", "dedupe_signature": "78f633a691ea900c4c3f758bdf7c3cac9d366d1361a573cf77af0e800f06493a", "difficulty": "easy", "final_answer": {"answer": 380.4422, "unit": "W"}, "id": "ohm_power_006287_154.2_62.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 62.5 ohm and voltage 154.2 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=154.2 V and R=62.5 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 62.5, "voltage": 154.2}, "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) = -0.45 y, so each step multiplies y by 1 - h*0.45.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0004, \"unit\": \"state_units\"}", "dedupe_signature": "a299ec9701860e93a1140a68461573f0cefb6278dde4cb8cfc358d3428cdece0", "difficulty": "medium", "final_answer": {"answer": 0.0004, "unit": "state_units"}, "id": "euler_decay_006291_65.5_0.45_1.4_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.45 y with y(0)=65.5, step size h=1.4, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 65.5, "rate": 0.45, "step": 1.4, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.207, -0.845, 2.344], \"unit\": \"temperature_units\"}", "dedupe_signature": "5ccf0a7330918fcb2fa88dbf0346efd7bb68103d080c43f525531e59c384ead7", "difficulty": "hard", "final_answer": {"answer": [1.207, -0.845, 2.344], "unit": "temperature_units"}, "id": "heat_step_006293_0.06_0.1_1.45_-1.25_2.8_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=-0.75; current interior values are [1.45, -1.25, 2.8]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [1.45, -1.25, 2.8], "left": 0.1, "r": 0.06, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "909ec4f4a14d2355789e9b3cadb335e750a6c5e00a206f796fd9e0cb90069923", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006297_consistent_4153435f_763477", "license": "Apache-2.0", "prompt": "In lab notebook case 763477, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "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 = 2.49 * 8.314 * 256 / 3.7.\nFinal: {\"answer\": 1432.3449, \"unit\": \"kPa\"}", "dedupe_signature": "1e9450e033a2cf8ce7e53d1b01d1cc4df79d4feaab1a60dc01bb7b041e068376", "difficulty": "medium", "final_answer": {"answer": 1432.3449, "unit": "kPa"}, "id": "ideal_gas_006303_2.49_256_3.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.49 mol, T=256 K, and V=3.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.49 * 8.314 * 256 / 3.7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.49, "temp_k": 256, "volume_l": 3.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "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 2956.0 / 100.\nFinal: {\"answer\": 29.56, \"unit\": \"m\"}", "dedupe_signature": "cac68638a6d7e41d08645a46aa7bd6ac72e7c0d0fda8d9d70a5de8d08368c91a", "difficulty": "easy", "final_answer": {"answer": 29.56, "unit": "m"}, "id": "unit_convert_006312_cm_to_m_2956", "license": "Apache-2.0", "prompt": "Convert 2956 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 2956.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 2956.0}, "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 = 19.4 kg and a = 11.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 230.86, \"unit\": \"N\"}", "dedupe_signature": "c762bed285f9b506c90be44a3251c2d9098b338d3180ba09bf5042e49932fcc4", "difficulty": "easy", "final_answer": {"answer": 230.86, "unit": "N"}, "id": "force_006318_19.4_11.9", "license": "Apache-2.0", "prompt": "A cart has mass 19.4 kg and measured acceleration 11.9 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 = 19.4 kg and a = 11.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.9, "mass": 19.4}, "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 = 20.75 kg and a = 1.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 32.1625, \"unit\": \"N\"}", "dedupe_signature": "7671ece1d1005752b80eb36f8226a1155b5c3a341bca6bf4c3842fdb44e2d1c4", "difficulty": "easy", "final_answer": {"answer": 32.1625, "unit": "N"}, "id": "force_006336_20.75_1.55", "license": "Apache-2.0", "prompt": "A cart has mass 20.75 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 = 20.75 kg and a = 1.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.55, "mass": 20.75}, "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 = 15.65 kg and a = 6.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 97.8125, \"unit\": \"N\"}", "dedupe_signature": "3786053f66ac15ce41e38aae45ceba616a5b063771f042c195fb6f23d13554c1", "difficulty": "easy", "final_answer": {"answer": 97.8125, "unit": "N"}, "id": "force_006372_15.65_6.25", "license": "Apache-2.0", "prompt": "A cart has mass 15.65 kg and measured acceleration 6.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.65 kg and a = 6.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.25, "mass": 15.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.4^2 and multiply by 0.5 * 23.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5289.438, \"unit\": \"J\"}", "dedupe_signature": "94840a257ca150561b2d0de2e791dd3ffd9086bba7e6f411e9912e64921a88ee", "difficulty": "easy", "final_answer": {"answer": 5289.438, "unit": "J"}, "id": "ke_006373_23.1_21.4", "license": "Apache-2.0", "prompt": "A body of mass 23.1 kg moves at 21.4 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 = 21.4^2 and multiply by 0.5 * 23.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.1, "velocity": 21.4}, "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=0.28 and add it to the current value.\nFinal: {\"answer\": [0.444, 0.81, 1.374], \"unit\": \"temperature_units\"}", "dedupe_signature": "8791eb70eb2ea75d89856a0a2bc268b358de880c9699755c573f9d55173c9bf9", "difficulty": "hard", "final_answer": {"answer": [0.444, 0.81, 1.374], "unit": "temperature_units"}, "id": "heat_step_006383_0.28_1.45_0.15_-0.1_2.9_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=0.45; current interior values are [0.15, -0.1, 2.9]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [0.15, -0.1, 2.9], "left": 1.45, "r": 0.28, "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 finite_differences_006388(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_006388\"}", "dedupe_signature": "bd97575a8da3b53a263456f1eae7f18c8fe61defba86b28d75e5f5a314412bc5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_006388"}, "id": "code_006388_finite_differences_006388", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_006388(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": "test", "task_family": "python_code_generation", "variables": {"function": "finite_differences_006388"}, "verifier": {"function": "finite_differences_006388", "tests": ["assert finite_differences_006388([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_006388([5]) == []", "assert finite_differences_006388([]) == []"], "type": "python_tests"}}
{"category": "science_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": "a6d386d98f4d630a5b0ba32da1af60320b7a567a5d4ef75a6ffc3d875b95abb6", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006389_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 57.4 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": "test", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.6 kg and a = 5.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 48.48, \"unit\": \"N\"}", "dedupe_signature": "e3c16a7ffca7c3fbefdcd76a670f1ee07f8a22401962f69a4f8713105a6f1c2d", "difficulty": "easy", "final_answer": {"answer": 48.48, "unit": "N"}, "id": "force_006390_9.6_5.05", "license": "Apache-2.0", "prompt": "A cart has mass 9.6 kg and measured acceleration 5.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.6 kg and a = 5.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.05, "mass": 9.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.2^2 and multiply by 0.5 * 29.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16989.021, \"unit\": \"J\"}", "dedupe_signature": "31776cb9165d59d7d7898691b8307be259baf5eede1ea993aff9b1a683753cf5", "difficulty": "easy", "final_answer": {"answer": 16989.021, "unit": "J"}, "id": "ke_006391_29.05_34.2", "license": "Apache-2.0", "prompt": "A body of mass 29.05 kg moves at 34.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.2^2 and multiply by 0.5 * 29.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.05, "velocity": 34.2}, "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. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "37540ba9c31c7bab2decb272d58d0e3444c95209bf32898c25086620da6a7e62", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006405_consistent_82e93f3d_279036", "license": "Apache-2.0", "prompt": "In sensor calibration case 279036, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "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=539 mg, t=81 h, and T_half=24 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 51.9532, \"unit\": \"mg\"}", "dedupe_signature": "95c8ca705db21f27387cab23318110dab7efc069bc2d05972202ca6647b3a5ca", "difficulty": "medium", "final_answer": {"answer": 51.9532, "unit": "mg"}, "id": "half_life_006414_539_24_81", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 539 mg. Its half-life is 24 hours. How many mg remain after 81 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=539 mg, t=81 h, and T_half=24 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 81.0, "half_life": 24.0, "initial_amount": 539.0}, "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 3904.5 / 100.\nFinal: {\"answer\": 39.045, \"unit\": \"m\"}", "dedupe_signature": "8165ea1ac72eab36d58cd372521b520fe581f8938eada0b2a07524d3dd4ffa5e", "difficulty": "easy", "final_answer": {"answer": 39.045, "unit": "m"}, "id": "unit_convert_006420_cm_to_m_3904.5", "license": "Apache-2.0", "prompt": "Convert 3904.5 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 3904.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 3904.5}, "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 = 39^2 and multiply by 0.5 * 12.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9164.025, \"unit\": \"J\"}", "dedupe_signature": "e392624725182038e5fd5657c19f53b855c2043ec6177be4af397dba63ad6f7e", "difficulty": "easy", "final_answer": {"answer": 9164.025, "unit": "J"}, "id": "ke_006427_12.05_39", "license": "Apache-2.0", "prompt": "A body of mass 12.05 kg moves at 39 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 39^2 and multiply by 0.5 * 12.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.05, "velocity": 39.0}, "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=968 mg, t=292 h, and T_half=43 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.7432, \"unit\": \"mg\"}", "dedupe_signature": "a2e24fe5794f8d12b25bcbaa48c78d1c556b1e8a41f29fe80b160b2a182f60d8", "difficulty": "medium", "final_answer": {"answer": 8.7432, "unit": "mg"}, "id": "half_life_006432_968_43_292", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 968 mg. Its half-life is 43 hours. How many mg remain after 292 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=968 mg, t=292 h, and T_half=43 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 292.0, "half_life": 43.0, "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. 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": "c0b2ab555cf440667f27e6ca6b9a272ab73d5a9d1e502b4ce1a1d4849a3bff3f", "difficulty": "medium", "final_answer": {"answer": [-1.55, -10.75], "unit": "dimensionless"}, "id": "line_two_point_006440_9.25_23.5_-1.55_-10.75", "license": "Apache-2.0", "prompt": "A line passes through points (9.25, -25.0875) and (23.5, -47.175). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 9.25, "x2": 23.5, "y1": -25.0875, "y2": -47.175000000000004}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 2.5467, \"unit\": \"state_units\"}", "dedupe_signature": "bfb02d792c8b240b13d5260dc0a0f900141511eb7a79f65ab628563e45d272d7", "difficulty": "medium", "final_answer": {"answer": 2.5467, "unit": "state_units"}, "id": "euler_decay_006453_53.5_0.35_0.75_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.35 y with y(0)=53.5, step size h=0.75, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 53.5, "rate": 0.35, "step": 0.75, "steps": 10}, "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 = 12.75 kg and a = 15.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 199.5375, \"unit\": \"N\"}", "dedupe_signature": "02bcfd3f56873e02e4b36d8f369c473cda3ecad47b0795f109c868c6363ccc20", "difficulty": "easy", "final_answer": {"answer": 199.5375, "unit": "N"}, "id": "force_006462_12.75_15.65", "license": "Apache-2.0", "prompt": "A cart has mass 12.75 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 = 12.75 kg and a = 15.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.65, "mass": 12.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=80 degrees through the sine of 2 theta.\n3. Substitute v=50.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 88.913, \"unit\": \"m\"}", "dedupe_signature": "42705eb44ee4bf113a37624929a440873963dd7cd76add51cc9713feee8e9234", "difficulty": "medium", "final_answer": {"answer": 88.913, "unit": "m"}, "id": "projectile_range_006464_50.5_80", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.5 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=80 degrees through the sine of 2 theta.\nSubstitute v=50.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 80, "gravity": 9.81, "speed": 50.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "f076ff1d5b5fccd40136df634d7e9c2589205094af7ddb498a336f8ae4f2c99c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_006497_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing clinical records in release 788933, 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": "test", "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 the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.86 * 8.314 * 494 / 68.7.\nFinal: {\"answer\": 111.197, \"unit\": \"kPa\"}", "dedupe_signature": "e23ca206f33a2da5f0b8cb2033b6fcb63d939b56cce36e89c77bcc069e1a10b0", "difficulty": "medium", "final_answer": {"answer": 111.197, "unit": "kPa"}, "id": "ideal_gas_006501_1.86_494_68.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.86 mol, T=494 K, and V=68.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.86 * 8.314 * 494 / 68.7.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 1.86, "temp_k": 494, "volume_l": 68.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=141.5 mg, t=157.5 h, and T_half=13.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0435, \"unit\": \"mg\"}", "dedupe_signature": "d9c8c256319ad58e77e9b1cd780ae45d468cfdc457fb88281378db45aa6f30f1", "difficulty": "medium", "final_answer": {"answer": 0.0435, "unit": "mg"}, "id": "half_life_006504_141.5_13.5_157.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 141.5 mg. Its half-life is 13.5 hours. How many mg remain after 157.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=141.5 mg, t=157.5 h, and T_half=13.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 157.5, "half_life": 13.5, "initial_amount": 141.5}, "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(7.6)=-24.82 and f(17.2)=-69.94.\n3. The interval width is 9.6.\nFinal: {\"answer\": -454.848, \"unit\": \"area_units\"}", "dedupe_signature": "8ffee186f820204cf24a3b9ec2d4115e03f2965edb80fa01486924a9f3c8215b", "difficulty": "medium", "final_answer": {"answer": -454.848, "unit": "area_units"}, "id": "trapz_linear_006508_-4.7_10.9_7.6_17.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.7x+10.9 from x=7.6 to x=17.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.6)=-24.82 and f(17.2)=-69.94.\nThe interval width is 9.6.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 10.9, "slope": -4.7, "x0": 7.6, "x1": 17.2}, "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=59 degrees through the sine of 2 theta.\n3. Substitute v=27.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 69.0598, \"unit\": \"m\"}", "dedupe_signature": "d25c88340ba09476e74218bbb0d4df60892c34cceb76c6b1b18e1dfe1c7e7b5e", "difficulty": "medium", "final_answer": {"answer": 69.0598, "unit": "m"}, "id": "projectile_range_006518_27.7_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 27.7 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=27.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 27.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=215.2 V and R=15.9 ohm.\nFinal: {\"answer\": 2912.644, \"unit\": \"W\"}", "dedupe_signature": "b4838a1558766ac825bd4897b79f0839b578332304304ff65f16ee07c3ebddda", "difficulty": "easy", "final_answer": {"answer": 2912.644, "unit": "W"}, "id": "ohm_power_006521_215.2_15.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 15.9 ohm and voltage 215.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=215.2 V and R=15.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 15.9, "voltage": 215.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.75 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 75.0653, \"unit\": \"g\"}", "dedupe_signature": "958d56f510acee2e3d85aeb6dc60c7af7bfbc7a0a9bdda373ca7ad076676ede0", "difficulty": "medium", "final_answer": {"answer": 75.0653, "unit": "g"}, "id": "stoich_mass_006523_calcium_carbonate_0.75", "license": "Apache-2.0", "prompt": "A sample contains 0.75 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.75 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.75}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 11.7048, \"unit\": \"state_units\"}", "dedupe_signature": "7272c1c5350f97e12bb836ca199e5bac035822626c893edadbc95b72e133a627", "difficulty": "medium", "final_answer": {"answer": 11.7048, "unit": "state_units"}, "id": "euler_decay_006525_15_0.07_0.35_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.07 y with y(0)=15, step size h=0.35, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 15.0, "rate": 0.07, "step": 0.35, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.8)=-5.1 and f(1.6)=20.1.\n3. The interval width is 8.4.\nFinal: {\"answer\": 63.0, \"unit\": \"area_units\"}", "dedupe_signature": "cb632c9e6eb04e9c0d52eca5e93402185932507a1c5c43bb228fd401b63bf166", "difficulty": "medium", "final_answer": {"answer": 63.0, "unit": "area_units"}, "id": "trapz_linear_006526_3_15.3_-6.8_1.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3x+15.3 from x=-6.8 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(-6.8)=-5.1 and f(1.6)=20.1.\nThe interval width is 8.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 15.3, "slope": 3.0, "x0": -6.8, "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. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=147 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-76.319, 49.5622], \"unit\": \"N\"}", "dedupe_signature": "8c8a98a6c503c1744b19e9742ffc74fede4db51fb37adad5e4464531464798cd", "difficulty": "medium", "final_answer": {"answer": [-76.319, 49.5622], "unit": "N"}, "id": "vector_components_006529_91_147", "license": "Apache-2.0", "prompt": "A vector has magnitude 91 N at 147 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=147 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 147, "magnitude": 91.0}, "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=46 degrees through the sine of 2 theta.\n3. Substitute v=57.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 335.6527, \"unit\": \"m\"}", "dedupe_signature": "11ef0aaaaee347c6000774175d0a07f89c086fb2a61d38565a3d16277e3fd137", "difficulty": "medium", "final_answer": {"answer": 335.6527, "unit": "m"}, "id": "projectile_range_006536_57.4_46", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 57.4 m/s and angle 46 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=46 degrees through the sine of 2 theta.\nSubstitute v=57.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 46, "gravity": 9.81, "speed": 57.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.91 y, so each step multiplies y by 1 - h*0.91.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 1.0795, \"unit\": \"state_units\"}", "dedupe_signature": "e14a166d16645fca6527ec5acc75782d351e476cd384c267c84567af6b3a558e", "difficulty": "medium", "final_answer": {"answer": 1.0795, "unit": "state_units"}, "id": "euler_decay_006561_3_0.91_1.95_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.91 y with y(0)=3, step size h=1.95, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.91 y, so each step multiplies y by 1 - h*0.91.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 3.0, "rate": 0.91, "step": 1.95, "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\": [1.05, 24.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "82ec13d7b4eab70d51148aa270b98c376d341c301f0294af75f27f7ba5c3b0c1", "difficulty": "medium", "final_answer": {"answer": [1.05, 24.5], "unit": "dimensionless"}, "id": "line_two_point_006566_-0.25_3.5_1.05_24.5", "license": "Apache-2.0", "prompt": "A line passes through points (-0.25, 24.2375) and (3.5, 28.175). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -0.25, "x2": 3.5, "y1": 24.2375, "y2": 28.175}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "97cc3d5a9ec96a0d3105a4413690059acb0d1f55f30919123d09fe04ff8b6d98", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006585_consistent_4153435f_318074", "license": "Apache-2.0", "prompt": "In simulation spec case 318074, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: 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": "6cedd67e6681650319303ceb8675aadf76c8ed5248524fb5abf46e2b68c9af0b", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006587_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 77.2 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": "test", "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 = 1.35^2 and multiply by 0.5 * 25.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 23.0546, \"unit\": \"J\"}", "dedupe_signature": "9ff02706041a5e93e8ac60c2e447f2861910fca532418c1d750e8b8dd5d9878c", "difficulty": "easy", "final_answer": {"answer": 23.0546, "unit": "J"}, "id": "ke_006589_25.3_1.35", "license": "Apache-2.0", "prompt": "A body of mass 25.3 kg moves at 1.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.35^2 and multiply by 0.5 * 25.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.3, "velocity": 1.35}, "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=642 mg, t=303.5 h, and T_half=55 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 14.0087, \"unit\": \"mg\"}", "dedupe_signature": "c57b4691f77cdad0ab18121002d589fa21a4be17b79d9853c50b9bc715b22f56", "difficulty": "medium", "final_answer": {"answer": 14.0087, "unit": "mg"}, "id": "half_life_006594_642_55_303.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 642 mg. Its half-life is 55 hours. How many mg remain after 303.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=642 mg, t=303.5 h, and T_half=55 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 303.5, "half_life": 55.0, "initial_amount": 642.0}, "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) = -0.57 y, so each step multiplies y by 1 - h*0.57.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0609, \"unit\": \"state_units\"}", "dedupe_signature": "ec0a86d5b9497d6c6b4e4fbf16cff14ddb8bdd0257348049dd932dd8c15d2904", "difficulty": "medium", "final_answer": {"answer": 0.0609, "unit": "state_units"}, "id": "euler_decay_006597_31_0.57_1.25_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.57 y with y(0)=31, step size h=1.25, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 31.0, "rate": 0.57, "step": 1.25, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"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": "e3971a834cde22203e3639fed56471b47a8be68c7bf8605a95d7d66d7c3b6cb1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006603_inconsistent_7481c798_558238", "license": "Apache-2.0", "prompt": "In simulation spec case 558238, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "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=52.7 V and R=162.9 ohm.\nFinal: {\"answer\": 17.049, \"unit\": \"W\"}", "dedupe_signature": "74798ac94921da1457e8d0608c992cd8c07c75d34b0b437c93d021ea07cdaf28", "difficulty": "easy", "final_answer": {"answer": 17.049, "unit": "W"}, "id": "ohm_power_006611_52.7_162.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 162.9 ohm and voltage 52.7 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=52.7 V and R=162.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 162.9, "voltage": 52.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=518 mg, t=328 h, and T_half=80.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 30.7449, \"unit\": \"mg\"}", "dedupe_signature": "3627b13ef8d13b19d24d6d2d55380e939da076ff5d831230d8ed0dafbe48a9e8", "difficulty": "medium", "final_answer": {"answer": 30.7449, "unit": "mg"}, "id": "half_life_006612_518_80.5_328", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 518 mg. Its half-life is 80.5 hours. How many mg remain after 328 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=518 mg, t=328 h, and T_half=80.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 328.0, "half_life": 80.5, "initial_amount": 518.0}, "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 = 380 * 4.5 * 72.\nFinal: {\"answer\": 123120.0, \"unit\": \"J\"}", "dedupe_signature": "4c3fb19e271cc846b16ecbe6df0a982d3bdb76c955dbeb68eedda8a1e4ccc584", "difficulty": "easy", "final_answer": {"answer": 123120.0, "unit": "J"}, "id": "heat_q_006646_380_4.5_72", "license": "Apache-2.0", "prompt": "A 380 g sample has specific heat 4.5 J/(g*K). How much heat is needed to raise its temperature by 72 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 380 * 4.5 * 72.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 72, "heat_capacity": 4.5, "mass_g": 380}, "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=664 mg, t=329 h, and T_half=83 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 42.5529, \"unit\": \"mg\"}", "dedupe_signature": "44d1b991e4c29b192ba7a8e07ee80cbe822aae8401b55f02c548d2ff77e6e388", "difficulty": "medium", "final_answer": {"answer": 42.5529, "unit": "mg"}, "id": "half_life_006648_664_83_329", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 664 mg. Its half-life is 83 hours. How many mg remain after 329 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=664 mg, t=329 h, and T_half=83 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 329.0, "half_life": 83.0, "initial_amount": 664.0}, "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(6.7)=24.08 and f(9)=29.6.\n3. The interval width is 2.3.\nFinal: {\"answer\": 61.732, \"unit\": \"area_units\"}", "dedupe_signature": "fc209540f24382bb05e3965c929443d854d05f1e473230600e1567915be150d3", "difficulty": "medium", "final_answer": {"answer": 61.732, "unit": "area_units"}, "id": "trapz_linear_006652_2.4_8_6.7_9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.4x+8 from x=6.7 to x=9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.7)=24.08 and f(9)=29.6.\nThe interval width is 2.3.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 8.0, "slope": 2.4, "x0": 6.7, "x1": 9.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.2, 12.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "3a036665e545408b21030a6172844983aa36b2bbb6ba097f1cce188f56ffd7a5", "difficulty": "medium", "final_answer": {"answer": [-6.2, 12.5], "unit": "dimensionless"}, "id": "line_two_point_006656_9.25_16_-6.2_12.5", "license": "Apache-2.0", "prompt": "A line passes through points (9.25, -44.85) and (16, -86.7). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 9.25, "x2": 16.0, "y1": -44.85, "y2": -86.7}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.5 kg and a = 11.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 208.125, \"unit\": \"N\"}", "dedupe_signature": "2652b34984482ab46b0a8f73b2be4fd8005af63892fabe55a97133f55648a3c7", "difficulty": "easy", "final_answer": {"answer": 208.125, "unit": "N"}, "id": "force_006660_18.5_11.25", "license": "Apache-2.0", "prompt": "A cart has mass 18.5 kg and measured acceleration 11.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.5 kg and a = 11.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.25, "mass": 18.5}, "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=786.5 mg, t=180 h, and T_half=41.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 38.9069, \"unit\": \"mg\"}", "dedupe_signature": "b48d32581db6f5f9ead18848ecc6de9c07a52713f78d4ee5d52e74b86451d895", "difficulty": "medium", "final_answer": {"answer": 38.9069, "unit": "mg"}, "id": "half_life_006684_786.5_41.5_180", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 786.5 mg. Its half-life is 41.5 hours. How many mg remain after 180 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=786.5 mg, t=180 h, and T_half=41.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 180.0, "half_life": 41.5, "initial_amount": 786.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3115.0 / 100.\nFinal: {\"answer\": 31.15, \"unit\": \"m\"}", "dedupe_signature": "c2684152c046eaf1b1bcca5eeb9a51268d84347d65ad1dc0924f67f3bfa76154", "difficulty": "easy", "final_answer": {"answer": 31.15, "unit": "m"}, "id": "unit_convert_006690_cm_to_m_3115", "license": "Apache-2.0", "prompt": "Convert 3115 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 3115.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 3115.0}, "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 = 2.5^2 and multiply by 0.5 * 18.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 56.5625, \"unit\": \"J\"}", "dedupe_signature": "1ddd5ed969ed441098a3167ac685c4906ee874919a9054e23b13d058c7f7213d", "difficulty": "easy", "final_answer": {"answer": 56.5625, "unit": "J"}, "id": "ke_006715_18.1_2.5", "license": "Apache-2.0", "prompt": "A body of mass 18.1 kg moves at 2.5 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 = 2.5^2 and multiply by 0.5 * 18.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.1, "velocity": 2.5}, "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) = -0.78 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\": -0.0189, \"unit\": \"state_units\"}", "dedupe_signature": "05596ceb4861a3b755e4f2fe69e999b15cbfeadbb6e93c5b58e5ff63e8a9b646", "difficulty": "medium", "final_answer": {"answer": -0.0189, "unit": "state_units"}, "id": "euler_decay_006723_58_0.78_1.9_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.78 y with y(0)=58, step size h=1.9, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.78 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": "test", "task_family": "numerical_ode", "variables": {"initial_y": 58.0, "rate": 0.78, "step": 1.9, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.97 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1075.5313, \"unit\": \"g\"}", "dedupe_signature": "87fa765e00ba6f6526adaf059cc4319ae1fefa376b7b0e8099db2635c7498b0a", "difficulty": "medium", "final_answer": {"answer": 1075.5313, "unit": "g"}, "id": "stoich_mass_006757_glucose_5.97", "license": "Apache-2.0", "prompt": "A sample contains 5.97 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 = 5.97 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.97}, "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 1267.5 / 100.\nFinal: {\"answer\": 12.675, \"unit\": \"m\"}", "dedupe_signature": "8862eb432519365b86d4424405e51ff4c3e4af4e0495f946eeb825f6656f3d6c", "difficulty": "easy", "final_answer": {"answer": 12.675, "unit": "m"}, "id": "unit_convert_006762_cm_to_m_1267.5", "license": "Apache-2.0", "prompt": "Convert 1267.5 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 1267.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 1267.5}, "verifier": {"formula": "value / 100", "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 205.5 + 273.15.\nFinal: {\"answer\": 478.65, \"unit\": \"K\"}", "dedupe_signature": "ae9a825e6b3c870346a8f03ca88b307639eb611720f2efacab92fee13234195b", "difficulty": "easy", "final_answer": {"answer": 478.65, "unit": "K"}, "id": "unit_convert_006780_c_to_k_205.5", "license": "Apache-2.0", "prompt": "Convert 205.5 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 205.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 205.5}, "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) = -0.61 y, so each step multiplies y by 1 - h*0.61.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 28.0391, \"unit\": \"state_units\"}", "dedupe_signature": "c5d659f3049ad1e8c6bcd82976a22b5bd3b1ad3a681afd16d219cd7106c6e5eb", "difficulty": "medium", "final_answer": {"answer": 28.0391, "unit": "state_units"}, "id": "euler_decay_006795_63.5_0.61_0.55_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.61 y with y(0)=63.5, 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) = -0.61 y, so each step multiplies y by 1 - h*0.61.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 63.5, "rate": 0.61, "step": 0.55, "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=0.1 and add it to the current value.\nFinal: {\"answer\": [-1.04, 0.78, -1.035], \"unit\": \"temperature_units\"}", "dedupe_signature": "a65b963b1ecc3a527ad3388a8d394c631338849d77b733f87f1298fe5acc99e5", "difficulty": "hard", "final_answer": {"answer": [-1.04, 0.78, -1.035], "unit": "temperature_units"}, "id": "heat_step_006797_0.1_-0.15_-1.45_1.35_-1.55_0.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.15, right=0.7; current interior values are [-1.45, 1.35, -1.55]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.45, 1.35, -1.55], "left": -0.15, "r": 0.1, "right": 0.7}, "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=217.9 V and R=27.4 ohm.\nFinal: {\"answer\": 1732.8617, \"unit\": \"W\"}", "dedupe_signature": "121a4c5d1266d4dbedf476883aef61f2f184c83e280a3f5da648a5b0f8b55f9f", "difficulty": "easy", "final_answer": {"answer": 1732.8617, "unit": "W"}, "id": "ohm_power_006809_217.9_27.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 27.4 ohm and voltage 217.9 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=217.9 V and R=27.4 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 27.4, "voltage": 217.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [0.466, 0.934, 1.432], \"unit\": \"temperature_units\"}", "dedupe_signature": "0455f76e312e692017703f0911cca7ab19e9d25700a598b4618f82cb50e6b732", "difficulty": "hard", "final_answer": {"answer": [0.466, 0.934, 1.432], "unit": "temperature_units"}, "id": "heat_step_006815_0.38_-1.65_1.15_2.15_-0.05_1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=1.65; current interior values are [1.15, 2.15, -0.05]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [1.15, 2.15, -0.05], "left": -1.65, "r": 0.38, "right": 1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "4866c63b2ebb72ec339f604bfbdebd932529cd51025118426da57188518348d0", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006819_consistent_8b38953d_631831", "license": "Apache-2.0", "prompt": "In student derivation case 631831, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "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=116.8 V and R=4.5 ohm.\nFinal: {\"answer\": 3031.6089, \"unit\": \"W\"}", "dedupe_signature": "6ef8ec068043563a4b95a12fcdecf3bf59b25e16de0388f6071f4f8c4a4e417a", "difficulty": "easy", "final_answer": {"answer": 3031.6089, "unit": "W"}, "id": "ohm_power_006845_116.8_4.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 4.5 ohm and voltage 116.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=116.8 V and R=4.5 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 4.5, "voltage": 116.8}, "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: 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": "b9e8c31c72d12fe55df0f1027ea7b85be3bf1c8f6440222af7803e431ecf69c7", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006857_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 1032 items and budget 8660, 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": "test", "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 Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 130 * 4.45 * 55.\nFinal: {\"answer\": 31817.5, \"unit\": \"J\"}", "dedupe_signature": "ec9bf1ca8e7410e76ed8c5d90f29c6293008cf8cf9334afb733c9fce1ec9bf49", "difficulty": "easy", "final_answer": {"answer": 31817.5, "unit": "J"}, "id": "heat_q_006862_130_4.45_55", "license": "Apache-2.0", "prompt": "A 130 g sample has specific heat 4.45 J/(g*K). How much heat is needed to raise its temperature by 55 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 130 * 4.45 * 55.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 55, "heat_capacity": 4.45, "mass_g": 130}, "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 safe_mean_006874(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_006874\"}", "dedupe_signature": "316181e18dc6694647ad19dfc4f33a284c5dcd7ad418b59d11036631324bd048", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_006874"}, "id": "code_006874_safe_mean_006874", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_006874(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_006874"}, "verifier": {"function": "safe_mean_006874", "tests": ["assert safe_mean_006874([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_006874(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_006874([])\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=46 degrees through the sine of 2 theta.\n3. Substitute v=68.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 472.4551, \"unit\": \"m\"}", "dedupe_signature": "17268d0b4b1381258cf874b40bcdffffeebd870b1abd5dedb88d3761ea744574", "difficulty": "medium", "final_answer": {"answer": 472.4551, "unit": "m"}, "id": "projectile_range_006878_68.1_46", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 68.1 m/s and angle 46 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=46 degrees through the sine of 2 theta.\nSubstitute v=68.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 46, "gravity": 9.81, "speed": 68.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.42 * 8.314 * 497 / 102.0.\nFinal: {\"answer\": 98.0351, \"unit\": \"kPa\"}", "dedupe_signature": "2a5215b2f2aac3745c4c690b86ed6aa4d1d595c7cbf2819366e536eb93f922df", "difficulty": "medium", "final_answer": {"answer": 98.0351, "unit": "kPa"}, "id": "ideal_gas_006879_2.42_497_102.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.42 mol, T=497 K, and V=102.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.42 * 8.314 * 497 / 102.0.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.42, "temp_k": 497, "volume_l": 102.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "2aa282bdc2b26607c519f0265e670935eebd8a0416d70659e4999d3b05407528", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006893_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=69 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": "test", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=69 degrees through the sine of 2 theta.\n3. Substitute v=52.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 189.4363, \"unit\": \"m\"}", "dedupe_signature": "44525c01aeaaed3fc97b9394e3bf3d80a6671c38792a5aa4626253f461c30d0e", "difficulty": "medium", "final_answer": {"answer": 189.4363, "unit": "m"}, "id": "projectile_range_006896_52.7_69", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 52.7 m/s and angle 69 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=69 degrees through the sine of 2 theta.\nSubstitute v=52.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 69, "gravity": 9.81, "speed": 52.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.86 * 8.314 * 443 / 117.8.\nFinal: {\"answer\": 183.2171, \"unit\": \"kPa\"}", "dedupe_signature": "1ce15f0cbbf5eacff4e53b763614d116da697a9fc4964d983dda78b6df4f10ce", "difficulty": "medium", "final_answer": {"answer": 183.2171, "unit": "kPa"}, "id": "ideal_gas_006897_5.86_443_117.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.86 mol, T=443 K, and V=117.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.86 * 8.314 * 443 / 117.8.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 5.86, "temp_k": 443, "volume_l": 117.8}, "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. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6317db85293138114170fe318f4f528997ea6985a065c13c779a2ba339de6255", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006909_inconsistent_7481c798_46252", "license": "Apache-2.0", "prompt": "In simulation spec case 46252, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "192485b534bfadaa8367f2f62402632291eb87b6fe5d8a186b28edfbb3f9ab2e", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006911_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 1353 items and budget 93415, 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": "test", "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 = 10.9 kg and a = 10.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 112.815, \"unit\": \"N\"}", "dedupe_signature": "0096c63171f3f6b9e4c4ce51d445362fab377c53af6f85579c82676c46e98a98", "difficulty": "easy", "final_answer": {"answer": 112.815, "unit": "N"}, "id": "force_006912_10.9_10.35", "license": "Apache-2.0", "prompt": "A cart has mass 10.9 kg and measured acceleration 10.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.9 kg and a = 10.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.35, "mass": 10.9}, "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 2370 mL to 2.37 L.\n3. Compute M = 0.71 / 2.37.\nFinal: {\"answer\": 0.2996, \"unit\": \"mol/L\"}", "dedupe_signature": "3905a766fc66a4028e67f96fcc6ddda7a8704bd2255356a394072f0d0a7b8730", "difficulty": "medium", "final_answer": {"answer": 0.2996, "unit": "mol/L"}, "id": "molarity_006920_0.71_2370", "license": "Apache-2.0", "prompt": "A solution contains 0.71 mol of solute in 2370 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2370 mL to 2.37 L.\nCompute M = 0.71 / 2.37.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 0.71, "volume_ml": 2370}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 9.2197, \"unit\": \"state_units\"}", "dedupe_signature": "fedd05210274d55b1339cdd54f3d520aad2a0240203682f8b44f85f141d12cb2", "difficulty": "medium", "final_answer": {"answer": 9.2197, "unit": "state_units"}, "id": "euler_decay_006939_11_0.35_0.05_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.35 y with y(0)=11, step size h=0.05, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 11.0, "rate": 0.35, "step": 0.05, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.23 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 230.1723, \"unit\": \"g\"}", "dedupe_signature": "fb5608d10f7522e01dc8d679548eb1dd1abc7e301d218796c98cd37bd353ffe6", "difficulty": "medium", "final_answer": {"answer": 230.1723, "unit": "g"}, "id": "stoich_mass_006955_carbon_dioxide_5.23", "license": "Apache-2.0", "prompt": "A sample contains 5.23 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.23 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.23}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4015 mL to 4.015 L.\n3. Compute M = 0.445 / 4.015.\nFinal: {\"answer\": 0.1108, \"unit\": \"mol/L\"}", "dedupe_signature": "4a8dc160596e8f7386db683901ec5d78616f79cc0c17de39b38528b30bed4a0d", "difficulty": "medium", "final_answer": {"answer": 0.1108, "unit": "mol/L"}, "id": "molarity_006956_0.445_4015", "license": "Apache-2.0", "prompt": "A solution contains 0.445 mol of solute in 4015 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4015 mL to 4.015 L.\nCompute M = 0.445 / 4.015.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 0.445, "volume_ml": 4015}, "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": "cbd69dac3b19383c0bb20b274dbea9b84293cc639ce22eb986707b38ae16c2ab", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_006983_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile invoice record from batch 767726 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": "test", "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. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 41807.0 / 1000.\nFinal: {\"answer\": 41.807, \"unit\": \"kg\"}", "dedupe_signature": "137b33a00530217579b72a3ac75937cc2ea74f8b2b5a9869badeaceab7f2bdf6", "difficulty": "easy", "final_answer": {"answer": 41.807, "unit": "kg"}, "id": "unit_convert_006996_g_to_kg_41807", "license": "Apache-2.0", "prompt": "Convert 41807 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 41807.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 41807.0}, "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=84 degrees and keep the unit as newtons.\nFinal: {\"answer\": [39.1459, 372.4484], \"unit\": \"N\"}", "dedupe_signature": "b3616f10520ed1a6657d283eb4c2f04844ebb359e2cab7795f953641bb48a34f", "difficulty": "medium", "final_answer": {"answer": [39.1459, 372.4484], "unit": "N"}, "id": "vector_components_006997_374.5_84", "license": "Apache-2.0", "prompt": "A vector has magnitude 374.5 N at 84 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=84 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 84, "magnitude": 374.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=451 mg, t=50.5 h, and T_half=88.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 303.6703, \"unit\": \"mg\"}", "dedupe_signature": "c30d9f341a68c282f0da9003c629f82904c06ee59ff4cc4aeaa28c1334110e96", "difficulty": "medium", "final_answer": {"answer": 303.6703, "unit": "mg"}, "id": "half_life_007008_451_88.5_50.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 451 mg. Its half-life is 88.5 hours. How many mg remain after 50.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=451 mg, t=50.5 h, and T_half=88.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 50.5, "half_life": 88.5, "initial_amount": 451.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.7 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 486.4212, \"unit\": \"g\"}", "dedupe_signature": "36354de9a8201277843b15fc5a097c0b54220b96a340c902f5138a029438a512", "difficulty": "medium", "final_answer": {"answer": 486.4212, "unit": "g"}, "id": "stoich_mass_007009_glucose_2.7", "license": "Apache-2.0", "prompt": "A sample contains 2.7 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 = 2.7 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.7}, "verifier": {"formula": "moles * molar_mass", "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": "58da845f35c019582e0c4d49a1e55c550799346b77a9b902b6e64a2cac6264b4", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_007019_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry clinical record from batch 787081 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": "test", "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 slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.45, -21.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "03335d5dfcfed9b51cb043f41abce355a7da20309eeff208438c8452e06d7dc5", "difficulty": "medium", "final_answer": {"answer": [2.45, -21.75], "unit": "dimensionless"}, "id": "line_two_point_007034_5.75_16.75_2.45_-21.75", "license": "Apache-2.0", "prompt": "A line passes through points (5.75, -7.6625) and (16.75, 19.2875). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 5.75, "x2": 16.75, "y1": -7.6625, "y2": 19.2875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.36 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1145.7922, \"unit\": \"g\"}", "dedupe_signature": "dc306f8ddfbcab8652a37c93e6f89b7603984dd21d5d5b04bad7f6b6f814ab98", "difficulty": "medium", "final_answer": {"answer": 1145.7922, "unit": "g"}, "id": "stoich_mass_007045_glucose_6.36", "license": "Apache-2.0", "prompt": "A sample contains 6.36 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 = 6.36 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.36}, "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 = 3.8^2 and multiply by 0.5 * 6.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 44.403, \"unit\": \"J\"}", "dedupe_signature": "a0f4cbb59f8fed69d1d2a11091fda92f12e2c8e063951734899d6b82909f56cf", "difficulty": "easy", "final_answer": {"answer": 44.403, "unit": "J"}, "id": "ke_007057_6.15_3.8", "license": "Apache-2.0", "prompt": "A body of mass 6.15 kg moves at 3.8 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 = 3.8^2 and multiply by 0.5 * 6.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.15, "velocity": 3.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.99 * 8.314 * 292 / 2.5.\nFinal: {\"answer\": 3874.59, \"unit\": \"kPa\"}", "dedupe_signature": "9868b563e78879a30abb4d5637a65d26b4740e2d35702b396ac885af53a8bf02", "difficulty": "medium", "final_answer": {"answer": 3874.59, "unit": "kPa"}, "id": "ideal_gas_007077_3.99_292_2.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.99 mol, T=292 K, and V=2.5 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 = 3.99 * 8.314 * 292 / 2.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.99, "temp_k": 292, "volume_l": 2.5}, "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 = 565 * 0.925 * 27.\nFinal: {\"answer\": 14110.875, \"unit\": \"J\"}", "dedupe_signature": "5b4928ab2f45f81f588d0b691f9d280559029029fb10e374fecde94f0c144894", "difficulty": "easy", "final_answer": {"answer": 14110.875, "unit": "J"}, "id": "heat_q_007078_565_0.925_27", "license": "Apache-2.0", "prompt": "A 565 g sample has specific heat 0.925 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 = 565 * 0.925 * 27.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 27, "heat_capacity": 0.925, "mass_g": 565}, "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\": [-2.0, -9.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0d281fb90a09c09d08a0fc911fcfae9bfcb0b308ecb48c83c65db06fae0c060f", "difficulty": "medium", "final_answer": {"answer": [-2.0, -9.75], "unit": "dimensionless"}, "id": "line_two_point_007088_-14_-2.25_-2_-9.75", "license": "Apache-2.0", "prompt": "A line passes through points (-14, 18.25) and (-2.25, -5.25). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -14.0, "x2": -2.25, "y1": 18.25, "y2": -5.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R 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 * 591 / 70.0.\nFinal: {\"answer\": 63.1745, \"unit\": \"kPa\"}", "dedupe_signature": "966c31f89663e36e90aed87c0ba290b0bbeae07af47bb7fb675809f6d9d759a1", "difficulty": "medium", "final_answer": {"answer": 63.1745, "unit": "kPa"}, "id": "ideal_gas_007095_0.9_591_70.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.9 mol, T=591 K, and V=70.0 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 = 0.9 * 8.314 * 591 / 70.0.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 0.9, "temp_k": 591, "volume_l": 70.0}, "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\nimport math\n\ndef unit_vector_007108(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_007108\"}", "dedupe_signature": "d2c30dee6df5f6726bd89170697f9824836ae34d6a6a782154990cd3eae4d20a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_007108"}, "id": "code_007108_unit_vector_007108", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_007108(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": "test", "task_family": "python_code_generation", "variables": {"function": "unit_vector_007108"}, "verifier": {"function": "unit_vector_007108", "tests": ["ux, uy = unit_vector_007108(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_007108(0, 5) == (0, 1)", "try:\n    unit_vector_007108(0, 0)\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=84 mg, t=328.5 h, and T_half=41.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.3479, \"unit\": \"mg\"}", "dedupe_signature": "94d374c57fa0c3c06bb02896d8b1b6e1d5b3862c9058135f35c1fae83007e37e", "difficulty": "medium", "final_answer": {"answer": 0.3479, "unit": "mg"}, "id": "half_life_007116_84_41.5_328.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 84 mg. Its half-life is 41.5 hours. How many mg remain after 328.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=84 mg, t=328.5 h, and T_half=41.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 328.5, "half_life": 41.5, "initial_amount": 84.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=11 mg, t=295.5 h, and T_half=64 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.4482, \"unit\": \"mg\"}", "dedupe_signature": "313c1721b0c04afb765b3c967b6fdf521e98b5674bf19458c60ee1ca8a4903c3", "difficulty": "medium", "final_answer": {"answer": 0.4482, "unit": "mg"}, "id": "half_life_007134_11_64_295.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 11 mg. Its half-life is 64 hours. How many mg remain after 295.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=11 mg, t=295.5 h, and T_half=64 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 295.5, "half_life": 64.0, "initial_amount": 11.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.03 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 545.8727, \"unit\": \"g\"}", "dedupe_signature": "77c24f03db4da60bb60780930b45e9a9242198196b6fc042746b3736815577b7", "difficulty": "medium", "final_answer": {"answer": 545.8727, "unit": "g"}, "id": "stoich_mass_007153_glucose_3.03", "license": "Apache-2.0", "prompt": "A sample contains 3.03 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 = 3.03 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.03}, "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 4250.0 / 100.\nFinal: {\"answer\": 42.5, \"unit\": \"m\"}", "dedupe_signature": "9fa21530f37b4cced0e975e7d6f8e8583d6b27252a9dc511bb8c0f20c9565156", "difficulty": "easy", "final_answer": {"answer": 42.5, "unit": "m"}, "id": "unit_convert_007176_cm_to_m_4250", "license": "Apache-2.0", "prompt": "Convert 4250 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 4250.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 4250.0}, "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 = 3.15 * 8.314 * 323 / 95.4.\nFinal: {\"answer\": 88.6696, \"unit\": \"kPa\"}", "dedupe_signature": "e6b99e426c22228ddf2857db6b913e384627014defe96266f1d4b24ec3c8e5bb", "difficulty": "medium", "final_answer": {"answer": 88.6696, "unit": "kPa"}, "id": "ideal_gas_007185_3.15_323_95.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.15 mol, T=323 K, and V=95.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.15 * 8.314 * 323 / 95.4.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 3.15, "temp_k": 323, "volume_l": 95.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=45.5 mg, t=3.5 h, and T_half=74 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 44.0325, \"unit\": \"mg\"}", "dedupe_signature": "96e505ca9b0341e640cca33ece5d51b8e571fa22ff4df5fe27a11d9b1f9fd50d", "difficulty": "medium", "final_answer": {"answer": 44.0325, "unit": "mg"}, "id": "half_life_007188_45.5_74_3.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 45.5 mg. Its half-life is 74 hours. How many mg remain after 3.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=45.5 mg, t=3.5 h, and T_half=74 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 3.5, "half_life": 74.0, "initial_amount": 45.5}, "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\": [-8.3, -12.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "28b28a32355c3a89b321205ed277914120f1c43dbbdf75640bbe2627dab713ec", "difficulty": "medium", "final_answer": {"answer": [-8.3, -12.0], "unit": "dimensionless"}, "id": "line_two_point_007196_0_4.25_-8.3_-12", "license": "Apache-2.0", "prompt": "A line passes through points (0, -12) and (4.25, -47.275). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 0.0, "x2": 4.25, "y1": -12.0, "y2": -47.275000000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_007216(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_007216\"}", "dedupe_signature": "72b5e8537480eaf0d0ef2980e8aae6823f0923d8bfcd4c625327519c4de081d4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_007216"}, "id": "code_007216_safe_mean_007216", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_007216(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": "test", "task_family": "python_code_generation", "variables": {"function": "safe_mean_007216"}, "verifier": {"function": "safe_mean_007216", "tests": ["assert safe_mean_007216([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_007216(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_007216([])\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=222.4 V and R=68 ohm.\nFinal: {\"answer\": 727.3788, \"unit\": \"W\"}", "dedupe_signature": "90581708860d84d82fdddb2981bc5bce78c7f9a8342201c677847936e8dbc5f1", "difficulty": "easy", "final_answer": {"answer": 727.3788, "unit": "W"}, "id": "ohm_power_007223_222.4_68", "license": "Apache-2.0", "prompt": "A resistor has resistance 68 ohm and voltage 222.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=222.4 V and R=68 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 68.0, "voltage": 222.4}, "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 320.0 / 100.\nFinal: {\"answer\": 3.2, \"unit\": \"m\"}", "dedupe_signature": "7548a6275ee0b20c9e39d1ef0f90ef28ba84be5f67db4a3c61ef679b907d10a9", "difficulty": "easy", "final_answer": {"answer": 3.2, "unit": "m"}, "id": "unit_convert_007230_cm_to_m_320", "license": "Apache-2.0", "prompt": "Convert 320 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 320.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 320.0}, "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=15 degrees through the sine of 2 theta.\n3. Substitute v=47.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 114.0311, \"unit\": \"m\"}", "dedupe_signature": "5928286fa1f2c5f2a909ba3570953770d8e622547ada1249558f1c1dfd5c08c4", "difficulty": "medium", "final_answer": {"answer": 114.0311, "unit": "m"}, "id": "projectile_range_007238_47.3_15", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 47.3 m/s and angle 15 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=15 degrees through the sine of 2 theta.\nSubstitute v=47.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 15, "gravity": 9.81, "speed": 47.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.5 * 8.314 * 497 / 74.2.\nFinal: {\"answer\": 139.2203, \"unit\": \"kPa\"}", "dedupe_signature": "b4b1e6304cef3189eec20ea57621c86c9404b1c761d012a8fa3a31bd0c7c0906", "difficulty": "medium", "final_answer": {"answer": 139.2203, "unit": "kPa"}, "id": "ideal_gas_007239_2.5_497_74.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.5 mol, T=497 K, and V=74.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.5 * 8.314 * 497 / 74.2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.5, "temp_k": 497, "volume_l": 74.2}, "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 = 20.95 kg and a = 4.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 87.99, \"unit\": \"N\"}", "dedupe_signature": "0b270f012eb57a04eb2b6b61aa93e4aaea5fa41b588aa7e944534e57dd7f34ec", "difficulty": "easy", "final_answer": {"answer": 87.99, "unit": "N"}, "id": "force_007254_20.95_4.2", "license": "Apache-2.0", "prompt": "A cart has mass 20.95 kg and measured acceleration 4.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.95 kg and a = 4.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.2, "mass": 20.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8.65^2 and multiply by 0.5 * 20.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 761.3189, \"unit\": \"J\"}", "dedupe_signature": "e195b0f21ee2db142af9f5854d5a7abfb4a273299c05302ebcbf4f9b18541303", "difficulty": "easy", "final_answer": {"answer": 761.3189, "unit": "J"}, "id": "ke_007255_20.35_8.65", "license": "Apache-2.0", "prompt": "A body of mass 20.35 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 * 20.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.35, "velocity": 8.65}, "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 = 7.86 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1416.0262, \"unit\": \"g\"}", "dedupe_signature": "8df44a9a948ffa81f67f04a67abda4ea5ca394f7be0a521d738f8a5ad776c887", "difficulty": "medium", "final_answer": {"answer": 1416.0262, "unit": "g"}, "id": "stoich_mass_007261_glucose_7.86", "license": "Apache-2.0", "prompt": "A sample contains 7.86 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 = 7.86 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.86}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4785 mL to 4.785 L.\n3. Compute M = 1.9 / 4.785.\nFinal: {\"answer\": 0.3971, \"unit\": \"mol/L\"}", "dedupe_signature": "e13877914506f0f4ea512c5989998c44f63836614a0aa3e31bbe92bf1031d6fe", "difficulty": "medium", "final_answer": {"answer": 0.3971, "unit": "mol/L"}, "id": "molarity_007262_1.9_4785", "license": "Apache-2.0", "prompt": "A solution contains 1.9 mol of solute in 4785 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4785 mL to 4.785 L.\nCompute M = 1.9 / 4.785.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.9, "volume_ml": 4785}, "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=34 degrees and keep the unit as newtons.\nFinal: {\"answer\": [147.5687, 99.5363], \"unit\": \"N\"}", "dedupe_signature": "aebb6ada4060ff6b5aa2da29e749e61cab6b4f5167658b669bc36cfd4abe961f", "difficulty": "medium", "final_answer": {"answer": [147.5687, 99.5363], "unit": "N"}, "id": "vector_components_007285_178_34", "license": "Apache-2.0", "prompt": "A vector has magnitude 178 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": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 34, "magnitude": 178.0}, "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. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0038, \"unit\": \"state_units\"}", "dedupe_signature": "194ecb7325659e6f86c7ed80751e73d22ff716d848c3286dc95d955bc46365c6", "difficulty": "medium", "final_answer": {"answer": 0.0038, "unit": "state_units"}, "id": "euler_decay_007299_31.5_0.54_1.1_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.54 y with y(0)=31.5, step size h=1.1, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 31.5, "rate": 0.54, "step": 1.1, "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\": [5.9, -26.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "339cf51c86dd9907a8a62b0c76464d2faa34e02ec6434c12d2360249b7b2e298", "difficulty": "medium", "final_answer": {"answer": [5.9, -26.0], "unit": "dimensionless"}, "id": "line_two_point_007304_-17_-6_5.9_-26", "license": "Apache-2.0", "prompt": "A line passes through points (-17, -126.3) and (-6, -61.4). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -17.0, "x2": -6.0, "y1": -126.30000000000001, "y2": -61.400000000000006}, "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 = 2.7 * 8.314 * 244 / 9.5.\nFinal: {\"answer\": 576.554, \"unit\": \"kPa\"}", "dedupe_signature": "5063356b9d9565a9c23ec8e4ea16447589bba8dfb262fb580e4693b91fc2f744", "difficulty": "medium", "final_answer": {"answer": 576.554, "unit": "kPa"}, "id": "ideal_gas_007311_2.7_244_9.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.7 mol, T=244 K, and V=9.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.7 * 8.314 * 244 / 9.5.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"n_mol": 2.7, "temp_k": 244, "volume_l": 9.5}, "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=63.2 V and R=165.8 ohm.\nFinal: {\"answer\": 24.0907, \"unit\": \"W\"}", "dedupe_signature": "f582e4f46a1afad72ea28e98bc913e2c69bceb04d5d3028139030e2bfc4b00f2", "difficulty": "easy", "final_answer": {"answer": 24.0907, "unit": "W"}, "id": "ohm_power_007313_63.2_165.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 165.8 ohm and voltage 63.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=63.2 V and R=165.8 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 165.8, "voltage": 63.2}, "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: 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": "59a49fa1506c96a95df73048a12fdb5b56b56b8b9ca64797a3ab122c223b871b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_007325_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry survey record from batch 276282 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": "test", "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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=606 mg, t=234 h, and T_half=111.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 141.4864, \"unit\": \"mg\"}", "dedupe_signature": "3579d2ef8fb8bfd1652667ae8aea5afb371d55b1736b2c3e7567000be1f06127", "difficulty": "medium", "final_answer": {"answer": 141.4864, "unit": "mg"}, "id": "half_life_007350_606_111.5_234", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 606 mg. Its half-life is 111.5 hours. How many mg remain after 234 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=606 mg, t=234 h, and T_half=111.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 234.0, "half_life": 111.5, "initial_amount": 606.0}, "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=137.2 V and R=157.9 ohm.\nFinal: {\"answer\": 119.2137, \"unit\": \"W\"}", "dedupe_signature": "29f79fd0fc61fb1be8a1c59d6a15831adbe7ff33ab395405a09c8cfabb235af4", "difficulty": "easy", "final_answer": {"answer": 119.2137, "unit": "W"}, "id": "ohm_power_007367_137.2_157.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 157.9 ohm and voltage 137.2 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=137.2 V and R=157.9 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 157.9, "voltage": 137.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.91 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 345.3804, \"unit\": \"g\"}", "dedupe_signature": "740049d36db033c765bdc2266b35ac588005afb2f14056573269aa4955531ed1", "difficulty": "medium", "final_answer": {"answer": 345.3804, "unit": "g"}, "id": "stoich_mass_007369_sodium_chloride_5.91", "license": "Apache-2.0", "prompt": "A sample contains 5.91 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.91 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.91}, "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\": [-0.071, -0.547, -0.826], \"unit\": \"temperature_units\"}", "dedupe_signature": "79152a9533e2e9ac365b7fa4e780098f960376b4bc307a881cef9bfa974731ff", "difficulty": "hard", "final_answer": {"answer": [-0.071, -0.547, -0.826], "unit": "temperature_units"}, "id": "heat_step_007373_0.38_1.0_0.1_-1.25_-0.75_-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, right=-0.45; current interior values are [0.1, -1.25, -0.75]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [0.1, -1.25, -0.75], "left": 1.0, "r": 0.38, "right": -0.45}, "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 1245 mL to 1.245 L.\n3. Compute M = 4.085 / 1.245.\nFinal: {\"answer\": 3.2811, \"unit\": \"mol/L\"}", "dedupe_signature": "334ddd7eb98ddca6ca5bd2052c4cbb790869f8b636c2024ae6f261c5b6f98c0e", "difficulty": "medium", "final_answer": {"answer": 3.2811, "unit": "mol/L"}, "id": "molarity_007388_4.085_1245", "license": "Apache-2.0", "prompt": "A solution contains 4.085 mol of solute in 1245 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1245 mL to 1.245 L.\nCompute M = 4.085 / 1.245.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.085, "volume_ml": 1245}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.6422, \"unit\": \"state_units\"}", "dedupe_signature": "54233286b1fa5f5c78d7c389fa39fa5a6db76e643f9434a31cf86efd382f30e5", "difficulty": "medium", "final_answer": {"answer": 0.6422, "unit": "state_units"}, "id": "euler_decay_007389_45_0.29_1.75_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.29 y with y(0)=45, step size h=1.75, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_ode", "variables": {"initial_y": 45.0, "rate": 0.29, "step": 1.75, "steps": 6}, "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\": [-0.25, -23.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "e97c725df32c66c347fc3641403a02fa7f79eddc8448f829cd8a579e3b718428", "difficulty": "medium", "final_answer": {"answer": [-0.25, -23.75], "unit": "dimensionless"}, "id": "line_two_point_007394_-9.25_2.25_-0.25_-23.75", "license": "Apache-2.0", "prompt": "A line passes through points (-9.25, -21.4375) and (2.25, -24.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -9.25, "x2": 2.25, "y1": -21.4375, "y2": -24.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a 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_007396(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_007396\"}", "dedupe_signature": "3dd80268040b04f9d8cabdedc10b3c3656681c42e61abc8058badf158c534be5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007396"}, "id": "code_007396_center_values_007396", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007396(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": "test", "task_family": "python_code_generation", "variables": {"function": "center_values_007396"}, "verifier": {"function": "center_values_007396", "tests": ["out = center_values_007396([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007396([5]) == [0]", "try:\n    center_values_007396([])\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 = 680 * 1.905 * 84.\nFinal: {\"answer\": 108813.6, \"unit\": \"J\"}", "dedupe_signature": "db130c5f27b41b676b0648c7d58a7197ecb93ffc500c050f74bed15fc842c3d9", "difficulty": "easy", "final_answer": {"answer": 108813.6, "unit": "J"}, "id": "heat_q_007402_680_1.905_84", "license": "Apache-2.0", "prompt": "A 680 g sample has specific heat 1.905 J/(g*K). How much heat is needed to raise its temperature by 84 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 680 * 1.905 * 84.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 84, "heat_capacity": 1.905, "mass_g": 680}, "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 675 mL to 0.675 L.\n3. Compute M = 4.685 / 0.675.\nFinal: {\"answer\": 6.9407, \"unit\": \"mol/L\"}", "dedupe_signature": "d256ee5c4602e90a995bbbbf8cc882f9759de588930215cde37a920e68bf113a", "difficulty": "medium", "final_answer": {"answer": 6.9407, "unit": "mol/L"}, "id": "molarity_007424_4.685_675", "license": "Apache-2.0", "prompt": "A solution contains 4.685 mol of solute in 675 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 675 mL to 0.675 L.\nCompute M = 4.685 / 0.675.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 4.685, "volume_ml": 675}, "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 = 8.2^2 and multiply by 0.5 * 7.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 260.555, \"unit\": \"J\"}", "dedupe_signature": "c9956b64aff21f2af40639cee57d6fbf23ece832e0908e2bb33c9daf18b499d1", "difficulty": "easy", "final_answer": {"answer": 260.555, "unit": "J"}, "id": "ke_007435_7.75_8.2", "license": "Apache-2.0", "prompt": "A body of mass 7.75 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 * 7.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.75, "velocity": 8.2}, "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\": [0.55, -28.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "4c3ee1ba507f065545f0d39ee3ec720e6172e649bf61db6899b89fdfac3883d0", "difficulty": "medium", "final_answer": {"answer": [0.55, -28.0], "unit": "dimensionless"}, "id": "line_two_point_007448_5.5_10.25_0.55_-28", "license": "Apache-2.0", "prompt": "A line passes through points (5.5, -24.975) and (10.25, -22.3625). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 5.5, "x2": 10.25, "y1": -24.975, "y2": -22.3625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.75 kg and a = 14.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 138.9375, \"unit\": \"N\"}", "dedupe_signature": "9cf9d1a41245c256e2c7e74604b7066dc3ebf301ef474d64703f73b6add4ac57", "difficulty": "easy", "final_answer": {"answer": 138.9375, "unit": "N"}, "id": "force_007452_9.75_14.25", "license": "Apache-2.0", "prompt": "A cart has mass 9.75 kg and measured acceleration 14.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.75 kg and a = 14.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.25, "mass": 9.75}, "verifier": {"formula": "mass * acceleration", "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 3390.5 / 100.\nFinal: {\"answer\": 33.905, \"unit\": \"m\"}", "dedupe_signature": "46b9ee001b51eb87ab1b864bdc21479fe09d0b808e1b5dd13e7766defcb3cbbf", "difficulty": "easy", "final_answer": {"answer": 33.905, "unit": "m"}, "id": "unit_convert_007464_cm_to_m_3390.5", "license": "Apache-2.0", "prompt": "Convert 3390.5 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 3390.5 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 3390.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.9, 19.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "0a9ecd082b64b76981c82c561cb3b9f69a7cfb25128d1c0ab4174c8d69191b32", "difficulty": "medium", "final_answer": {"answer": [6.9, 19.25], "unit": "dimensionless"}, "id": "line_two_point_007466_-20_-7.25_6.9_19.25", "license": "Apache-2.0", "prompt": "A line passes through points (-20, -118.75) and (-7.25, -30.775). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": -20.0, "x2": -7.25, "y1": -118.75, "y2": -30.775000000000006}, "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 = 5.55 kg and a = 1.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 8.88, \"unit\": \"N\"}", "dedupe_signature": "093eb63aacaa23e73524d537adc4bd9c562b54c87b38bacedaac435d7145baf5", "difficulty": "easy", "final_answer": {"answer": 8.88, "unit": "N"}, "id": "force_007470_5.55_1.6", "license": "Apache-2.0", "prompt": "A cart has mass 5.55 kg and measured acceleration 1.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.55 kg and a = 1.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.6, "mass": 5.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=23 degrees through the sine of 2 theta.\n3. Substitute v=28.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 59.9787, \"unit\": \"m\"}", "dedupe_signature": "e22282e5d9f4d6696dfaf7acfaacb8b30ef48328908ef858902c3dca4c2143ce", "difficulty": "medium", "final_answer": {"answer": 59.9787, "unit": "m"}, "id": "projectile_range_007472_28.6_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 28.6 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=23 degrees through the sine of 2 theta.\nSubstitute v=28.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 28.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=347 degrees and keep the unit as newtons.\nFinal: {\"answer\": [190.0022, -43.8655], \"unit\": \"N\"}", "dedupe_signature": "46303cc0e3135011e68681e85977dac7b78343f21c13b7b382705200ce5c1cfa", "difficulty": "medium", "final_answer": {"answer": [190.0022, -43.8655], "unit": "N"}, "id": "vector_components_007483_195_347", "license": "Apache-2.0", "prompt": "A vector has magnitude 195 N at 347 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=347 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 347, "magnitude": 195.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=996 mg, t=270 h, and T_half=22 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.2013, \"unit\": \"mg\"}", "dedupe_signature": "12ef2264379e368515f138b476687c7e03f800187dc0d69fdf69ee2335da5354", "difficulty": "medium", "final_answer": {"answer": 0.2013, "unit": "mg"}, "id": "half_life_007494_996_22_270", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 996 mg. Its half-life is 22 hours. How many mg remain after 270 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=996 mg, t=270 h, and T_half=22 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 270.0, "half_life": 22.0, "initial_amount": 996.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.74 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 674.5864, \"unit\": \"g\"}", "dedupe_signature": "1ead6eebcdf693960b4584f7dc0e21c4a536dcaec09f4993b9a1fc66b7619659", "difficulty": "medium", "final_answer": {"answer": 674.5864, "unit": "g"}, "id": "stoich_mass_007495_calcium_carbonate_6.74", "license": "Apache-2.0", "prompt": "A sample contains 6.74 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 = 6.74 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.74}, "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 = 5.32 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 95.8398, \"unit\": \"g\"}", "dedupe_signature": "64ff89a66981626cc628c007ee990f3be0b2f021ceb8157ee0de6ce9057c0510", "difficulty": "medium", "final_answer": {"answer": 95.8398, "unit": "g"}, "id": "stoich_mass_007513_water_5.32", "license": "Apache-2.0", "prompt": "A sample contains 5.32 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.32 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 5.32}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2115 mL to 2.115 L.\n3. Compute M = 2.68 / 2.115.\nFinal: {\"answer\": 1.2671, \"unit\": \"mol/L\"}", "dedupe_signature": "592a6c02f3b14120405bc80b8842b01ed977d7b7e4e877eed13125b4d81ff73f", "difficulty": "medium", "final_answer": {"answer": 1.2671, "unit": "mol/L"}, "id": "molarity_007514_2.68_2115", "license": "Apache-2.0", "prompt": "A solution contains 2.68 mol of solute in 2115 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2115 mL to 2.115 L.\nCompute M = 2.68 / 2.115.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.68, "volume_ml": 2115}, "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 9655.0 / 1000.\nFinal: {\"answer\": 9.655, \"unit\": \"kg\"}", "dedupe_signature": "12e26123b271baf2cd73f6a9e95649f712022ec9a1bd845deae3ae736325b1ac", "difficulty": "easy", "final_answer": {"answer": 9.655, "unit": "kg"}, "id": "unit_convert_007518_g_to_kg_9655", "license": "Apache-2.0", "prompt": "Convert 9655 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 9655.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 9655.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.45 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 376.938, \"unit\": \"g\"}", "dedupe_signature": "7e5d49b9b43a11d581de417f4f15bc46e287f2b74b6651e70f6ac4038e00f3ad", "difficulty": "medium", "final_answer": {"answer": 376.938, "unit": "g"}, "id": "stoich_mass_007531_sodium_chloride_6.45", "license": "Apache-2.0", "prompt": "A sample contains 6.45 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.45 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.45}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4340 mL to 4.34 L.\n3. Compute M = 1.86 / 4.34.\nFinal: {\"answer\": 0.4286, \"unit\": \"mol/L\"}", "dedupe_signature": "fd650b86de8434ffdabf755b9647ade78973be074c6cecb9ffcfd9337f50d225", "difficulty": "medium", "final_answer": {"answer": 0.4286, "unit": "mol/L"}, "id": "molarity_007532_1.86_4340", "license": "Apache-2.0", "prompt": "A solution contains 1.86 mol of solute in 4340 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4340 mL to 4.34 L.\nCompute M = 1.86 / 4.34.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 1.86, "volume_ml": 4340}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1270 mL to 1.27 L.\n3. Compute M = 2.815 / 1.27.\nFinal: {\"answer\": 2.2165, \"unit\": \"mol/L\"}", "dedupe_signature": "4e5723fc7aafd2043c6e51bb00e584118c6e1d82e1ce81400808b7485d37286b", "difficulty": "medium", "final_answer": {"answer": 2.2165, "unit": "mol/L"}, "id": "molarity_007550_2.815_1270", "license": "Apache-2.0", "prompt": "A solution contains 2.815 mol of solute in 1270 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1270 mL to 1.27 L.\nCompute M = 2.815 / 1.27.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.815, "volume_ml": 1270}, "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 = 13.45 kg and a = 2.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 29.59, \"unit\": \"N\"}", "dedupe_signature": "90a862317bc26082c14f56ba8eb3b4e7ea9155baa97232dac25fd5abbcd5b63f", "difficulty": "easy", "final_answer": {"answer": 29.59, "unit": "N"}, "id": "force_007560_13.45_2.2", "license": "Apache-2.0", "prompt": "A cart has mass 13.45 kg and measured acceleration 2.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 13.45 kg and a = 2.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.2, "mass": 13.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=31 degrees through the sine of 2 theta.\n3. Substitute v=34.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 109.6268, \"unit\": \"m\"}", "dedupe_signature": "c7e3b773dba0c88bafd7018bf23c34f58325254e283b4c413d332c8bdbf68b79", "difficulty": "medium", "final_answer": {"answer": 109.6268, "unit": "m"}, "id": "projectile_range_007562_34.9_31", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 34.9 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=31 degrees through the sine of 2 theta.\nSubstitute v=34.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 31, "gravity": 9.81, "speed": 34.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=710.5 mg, t=161 h, and T_half=115.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 270.3625, \"unit\": \"mg\"}", "dedupe_signature": "566248d8235303a16fd3ab028424da100afadc0b2fa8c02e7811cb48e999bcc0", "difficulty": "medium", "final_answer": {"answer": 270.3625, "unit": "mg"}, "id": "half_life_007584_710.5_115.5_161", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 710.5 mg. Its half-life is 115.5 hours. How many mg remain after 161 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=710.5 mg, t=161 h, and T_half=115.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 161.0, "half_life": 115.5, "initial_amount": 710.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 13.3 kg and a = 6.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 89.775, \"unit\": \"N\"}", "dedupe_signature": "55c4eb3c40b24d12fb1f4a261b3cdf519cba6c9a6b51a031165b044c96401e50", "difficulty": "easy", "final_answer": {"answer": 89.775, "unit": "N"}, "id": "force_007614_13.3_6.75", "license": "Apache-2.0", "prompt": "A cart has mass 13.3 kg and measured acceleration 6.75 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 = 13.3 kg and a = 6.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.75, "mass": 13.3}, "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=334.5 mg, t=77.5 h, and T_half=116.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 210.9309, \"unit\": \"mg\"}", "dedupe_signature": "9a24a4efcaf4fa3f60f7bebcaf86009dfe57e5f11dc11756c206ffb39a721699", "difficulty": "medium", "final_answer": {"answer": 210.9309, "unit": "mg"}, "id": "half_life_007620_334.5_116.5_77.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 334.5 mg. Its half-life is 116.5 hours. How many mg remain after 77.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=334.5 mg, t=77.5 h, and T_half=116.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 77.5, "half_life": 116.5, "initial_amount": 334.5}, "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. 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": "eedbb383efbe5d669a4d2acdb28642dc7b96441c3c3f2ffb5c14942177dbb01b", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007629_consistent_b7d3eed1_804736", "license": "Apache-2.0", "prompt": "In field worksheet case 804736, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "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\": [-7.25, -18.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "636973a12b37343461ca2080e8015b682e71e347ecd2b0225ca8d079640c215b", "difficulty": "medium", "final_answer": {"answer": [-7.25, -18.75], "unit": "dimensionless"}, "id": "line_two_point_007646_1.75_3.25_-7.25_-18.75", "license": "Apache-2.0", "prompt": "A line passes through points (1.75, -31.4375) and (3.25, -42.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "linear_modeling", "variables": {"x1": 1.75, "x2": 3.25, "y1": -31.4375, "y2": -42.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.55^2 and multiply by 0.5 * 10.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9625.2577, \"unit\": \"J\"}", "dedupe_signature": "e2729461fc8a225a5cfa571cf6ba43b086c89a0b7378cfe57a679f11183ce6d3", "difficulty": "easy", "final_answer": {"answer": 9625.2577, "unit": "J"}, "id": "ke_007651_10.15_43.55", "license": "Apache-2.0", "prompt": "A body of mass 10.15 kg moves at 43.55 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 = 43.55^2 and multiply by 0.5 * 10.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.15, "velocity": 43.55}, "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=690 mg, t=289 h, and T_half=20.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0394, \"unit\": \"mg\"}", "dedupe_signature": "e30bb688be4186372e479c188cbe56d517f51744a19fd956475f496cf2991011", "difficulty": "medium", "final_answer": {"answer": 0.0394, "unit": "mg"}, "id": "half_life_007674_690_20.5_289", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 690 mg. Its half-life is 20.5 hours. How many mg remain after 289 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=690 mg, t=289 h, and T_half=20.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 289.0, "half_life": 20.5, "initial_amount": 690.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=272 degrees and keep the unit as newtons.\nFinal: {\"answer\": [0.6456, -18.4887], \"unit\": \"N\"}", "dedupe_signature": "8630408ee082d6247c7273c7bef6e0ffc958cb70567d22dc0225efa56f0eaa06", "difficulty": "medium", "final_answer": {"answer": [0.6456, -18.4887], "unit": "N"}, "id": "vector_components_007681_18.5_272", "license": "Apache-2.0", "prompt": "A vector has magnitude 18.5 N at 272 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=272 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 272, "magnitude": 18.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 835 * 2.09 * 103.\nFinal: {\"answer\": 179750.45, \"unit\": \"J\"}", "dedupe_signature": "723132955518cf3cf437d1d1756f92e92e26589b727ac0c35dc46681bd70af10", "difficulty": "easy", "final_answer": {"answer": 179750.45, "unit": "J"}, "id": "heat_q_007690_835_2.09_103", "license": "Apache-2.0", "prompt": "A 835 g sample has specific heat 2.09 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 = 835 * 2.09 * 103.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "thermodynamics", "variables": {"delta_t": 103, "heat_capacity": 2.09, "mass_g": 835}, "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(4.7)=-15.88 and f(11.3)=-58.12.\n3. The interval width is 6.6.\nFinal: {\"answer\": -244.2, \"unit\": \"area_units\"}", "dedupe_signature": "7ac325b98e626cef413ffd0742ca054030cf3eabd99019aeea48d9d154dc3ae0", "difficulty": "medium", "final_answer": {"answer": -244.2, "unit": "area_units"}, "id": "trapz_linear_007696_-6.4_14.2_4.7_11.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.4x+14.2 from x=4.7 to x=11.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.7)=-15.88 and f(11.3)=-58.12.\nThe interval width is 6.6.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "numerical_integration", "variables": {"intercept": 14.2, "slope": -6.4, "x0": 4.7, "x1": 11.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.05, 13.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "fcffacc7edc8cef0bc526f8fedb5769d898a54078632362d05197da7ed1af3c4", "difficulty": "medium", "final_answer": {"answer": [7.05, 13.0], "unit": "dimensionless"}, "id": "line_two_point_007700_-17_-14.25_7.05_13", "license": "Apache-2.0", "prompt": "A line passes through points (-17, -106.85) and (-14.25, -87.4625). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -17.0, "x2": -14.25, "y1": -106.85, "y2": -87.46249999999999}, "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 = 5.1^2 and multiply by 0.5 * 29.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 380.3962, \"unit\": \"J\"}", "dedupe_signature": "99238e1bfdff51dde00b28bd87e5711e9d3b367029692ec33ce9376430ae48a3", "difficulty": "easy", "final_answer": {"answer": 380.3962, "unit": "J"}, "id": "ke_007705_29.25_5.1", "license": "Apache-2.0", "prompt": "A body of mass 29.25 kg moves at 5.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.1^2 and multiply by 0.5 * 29.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.25, "velocity": 5.1}, "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=524 mg, t=179.5 h, and T_half=113 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 174.2394, \"unit\": \"mg\"}", "dedupe_signature": "8ce4ce2d6322302b1d34d5f8448a0037929b2db044bc93479e6ae9191c6a8db1", "difficulty": "medium", "final_answer": {"answer": 174.2394, "unit": "mg"}, "id": "half_life_007710_524_113_179.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 524 mg. Its half-life is 113 hours. How many mg remain after 179.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=524 mg, t=179.5 h, and T_half=113 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 179.5, "half_life": 113.0, "initial_amount": 524.0}, "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 221.0 / 100.\nFinal: {\"answer\": 2.21, \"unit\": \"m\"}", "dedupe_signature": "bafbe6cf5b3676bfa10f7d360d5c79d522e49c65a6459ab74ef9f7588f5937be", "difficulty": "easy", "final_answer": {"answer": 2.21, "unit": "m"}, "id": "unit_convert_007716_cm_to_m_221", "license": "Apache-2.0", "prompt": "Convert 221 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 221.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 221.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=128 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-44.0198, 56.3428], \"unit\": \"N\"}", "dedupe_signature": "2504f858a5456cc7f83037807d714d5f45872cbd0787ed38c390a54631febe3c", "difficulty": "medium", "final_answer": {"answer": [-44.0198, 56.3428], "unit": "N"}, "id": "vector_components_007717_71.5_128", "license": "Apache-2.0", "prompt": "A vector has magnitude 71.5 N at 128 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=128 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 128, "magnitude": 71.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [-0.028, 1.256, 1.81], \"unit\": \"temperature_units\"}", "dedupe_signature": "33a07f0ab6de7489e6b00b91f5a0056eca194a93804b1fd47e02ecff121d7cdf", "difficulty": "hard", "final_answer": {"answer": [-0.028, 1.256, 1.81], "unit": "temperature_units"}, "id": "heat_step_007733_0.48_-0.9_0.5_0.8_2.05_2.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=2.8; current interior values are [0.5, 0.8, 2.05]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [0.5, 0.8, 2.05], "left": -0.9, "r": 0.48, "right": 2.8}, "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 = 11.6 kg and a = 9.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 109.04, \"unit\": \"N\"}", "dedupe_signature": "0ca10640c0a94ac83765d18a0e30cdbf68e0857304760b3c0d3f0b53ad7454c4", "difficulty": "easy", "final_answer": {"answer": 109.04, "unit": "N"}, "id": "force_007740_11.6_9.4", "license": "Apache-2.0", "prompt": "A cart has mass 11.6 kg and measured acceleration 9.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.6 kg and a = 9.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.4, "mass": 11.6}, "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=67 degrees through the sine of 2 theta.\n3. Substitute v=64.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 303.1706, \"unit\": \"m\"}", "dedupe_signature": "e7ddc4eb0c664fdb84bdc1f7f36e82ffbabff8de7f833e7bac9b366ec6c871e2", "difficulty": "medium", "final_answer": {"answer": 303.1706, "unit": "m"}, "id": "projectile_range_007742_64.3_67", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 64.3 m/s and angle 67 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=67 degrees through the sine of 2 theta.\nSubstitute v=64.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 67, "gravity": 9.81, "speed": 64.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=984.5 mg, t=165 h, and T_half=68.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 185.3988, \"unit\": \"mg\"}", "dedupe_signature": "5a70f319a23855c7c8348521bfad7662899be687525fb2c325a7ec4f508a92ab", "difficulty": "medium", "final_answer": {"answer": 185.3988, "unit": "mg"}, "id": "half_life_007782_984.5_68.5_165", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 984.5 mg. Its half-life is 68.5 hours. How many mg remain after 165 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=984.5 mg, t=165 h, and T_half=68.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 165.0, "half_life": 68.5, "initial_amount": 984.5}, "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 normalize_007792(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_007792\"}", "dedupe_signature": "fb35b50290f85a117a211cc2e42526c7cb4f426e5b1b0a8568ff54fbcc6feab9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007792"}, "id": "code_007792_normalize_007792", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007792(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": "test", "task_family": "python_code_generation", "variables": {"function": "normalize_007792"}, "verifier": {"function": "normalize_007792", "tests": ["out = normalize_007792([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007792([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007792([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007792([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=73 degrees through the sine of 2 theta.\n3. Substitute v=81.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 375.8415, \"unit\": \"m\"}", "dedupe_signature": "c91c11b60ee790b57cfddb36f0e673bb243dba57ae2e2d1c65dca03ab792e7fe", "difficulty": "medium", "final_answer": {"answer": 375.8415, "unit": "m"}, "id": "projectile_range_007796_81.2_73", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.2 m/s and angle 73 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=73 degrees through the sine of 2 theta.\nSubstitute v=81.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 73, "gravity": 9.81, "speed": 81.2}, "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=89 mg, t=85.5 h, and T_half=71 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 38.6262, \"unit\": \"mg\"}", "dedupe_signature": "a6b6956b8e8828e81465bf1439e44dec8b8668aa510bb4f91e5bb221f6f147fd", "difficulty": "medium", "final_answer": {"answer": 38.6262, "unit": "mg"}, "id": "half_life_007800_89_71_85.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 89 mg. Its half-life is 71 hours. How many mg remain after 85.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=89 mg, t=85.5 h, and T_half=71 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "exponential_decay", "variables": {"elapsed_time": 85.5, "half_life": 71.0, "initial_amount": 89.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "87f89b47bd0403bfa8db81fcf4434405c6bcf49e0b504258ccc7e846dfd65afe", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007809_consistent_82e93f3d_779641", "license": "Apache-2.0", "prompt": "In quality-control check case 779641, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.8 kg and a = 9.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 55.39, \"unit\": \"N\"}", "dedupe_signature": "5d950cb4c199bc61a176e3af76f0c248ede320bf2bec711618fd9fe3f1f1489b", "difficulty": "easy", "final_answer": {"answer": 55.39, "unit": "N"}, "id": "force_007812_5.8_9.55", "license": "Apache-2.0", "prompt": "A cart has mass 5.8 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 = 5.8 kg and a = 9.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.55, "mass": 5.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.95^2 and multiply by 0.5 * 29.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13387.7623, \"unit\": \"J\"}", "dedupe_signature": "ce5c17af34d6977b7ed53994cc286f047e97e2b88d2f17865e0ccc617fa2226c", "difficulty": "easy", "final_answer": {"answer": 13387.7623, "unit": "J"}, "id": "ke_007813_29.85_29.95", "license": "Apache-2.0", "prompt": "A body of mass 29.85 kg moves at 29.95 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 = 29.95^2 and multiply by 0.5 * 29.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.85, "velocity": 29.95}, "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 4559.0 / 100.\nFinal: {\"answer\": 45.59, \"unit\": \"m\"}", "dedupe_signature": "eaa19520ea4268a0761dfc18de989cf6f77e3850c7007fc756ceacd4c93dd65d", "difficulty": "easy", "final_answer": {"answer": 45.59, "unit": "m"}, "id": "unit_convert_007842_cm_to_m_4559", "license": "Apache-2.0", "prompt": "Convert 4559 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 4559.0 / 100.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_conversion", "variables": {"value": 4559.0}, "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 = 10.8^2 and multiply by 0.5 * 13.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 772.74, \"unit\": \"J\"}", "dedupe_signature": "4df1710ba81bec209b38add5b733d48a0cb1c894dcdbcfdffeddcec835337269", "difficulty": "easy", "final_answer": {"answer": 772.74, "unit": "J"}, "id": "ke_007849_13.25_10.8", "license": "Apache-2.0", "prompt": "A body of mass 13.25 kg moves at 10.8 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 = 10.8^2 and multiply by 0.5 * 13.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.25, "velocity": 10.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=72 degrees through the sine of 2 theta.\n3. Substitute v=81.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 395.0588, \"unit\": \"m\"}", "dedupe_signature": "b5ba27d30c5e630c4aac6a1ec6a75b5a09847180a6db70fdc26bf647db337a50", "difficulty": "medium", "final_answer": {"answer": 395.0588, "unit": "m"}, "id": "projectile_range_007850_81.2_72", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.2 m/s and angle 72 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=72 degrees through the sine of 2 theta.\nSubstitute v=81.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 72, "gravity": 9.81, "speed": 81.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=138.4 V and R=17.2 ohm.\nFinal: {\"answer\": 1113.6372, \"unit\": \"W\"}", "dedupe_signature": "8050a6c23a2b2bfb8a7c217e34e999f834ddbb18c5e037779888e5b0ba802c10", "difficulty": "easy", "final_answer": {"answer": 1113.6372, "unit": "W"}, "id": "ohm_power_007853_138.4_17.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 17.2 ohm and voltage 138.4 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=138.4 V and R=17.2 ohm.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "electric_circuits", "variables": {"resistance": 17.2, "voltage": 138.4}, "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=236 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-12.0226, -17.8243], \"unit\": \"N\"}", "dedupe_signature": "34f00b6a9aae6955a5f009b192f1724be1f20164686c573df1081c2b37babe5f", "difficulty": "medium", "final_answer": {"answer": [-12.0226, -17.8243], "unit": "N"}, "id": "vector_components_007861_21.5_236", "license": "Apache-2.0", "prompt": "A vector has magnitude 21.5 N at 236 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=236 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "vector_reasoning", "variables": {"angle_deg": 236, "magnitude": 21.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. 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": "e1a95834826e03af48d154e99d61a0cc0b2b8cc80b4e4d69db7748561fe8f2fb", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007881_consistent_8b38953d_877605", "license": "Apache-2.0", "prompt": "In simulation spec case 877605, 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": "test", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.4 kg and a = 10.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 174.66, \"unit\": \"N\"}", "dedupe_signature": "35911638ead8b5e49eae287890013a5b815de6c8a1255aef270d13ca1973f725", "difficulty": "easy", "final_answer": {"answer": 174.66, "unit": "N"}, "id": "force_007884_16.4_10.65", "license": "Apache-2.0", "prompt": "A cart has mass 16.4 kg and measured acceleration 10.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.4 kg and a = 10.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.65, "mass": 16.4}, "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=0.14 and add it to the current value.\nFinal: {\"answer\": [-1.195, -0.897, 0.277], \"unit\": \"temperature_units\"}", "dedupe_signature": "a52b19c7f1075db9df62dd317be42440ec64bc6fb6dc4b3cd047ec9ed38f0c7a", "difficulty": "hard", "final_answer": {"answer": [-1.195, -0.897, 0.277], "unit": "temperature_units"}, "id": "heat_step_007895_0.14_-0.75_-1.3_-1.1_0.55_0.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=0.25; current interior values are [-1.3, -1.1, 0.55]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-1.3, -1.1, 0.55], "left": -0.75, "r": 0.14, "right": 0.25}, "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\": [2.8, -8.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "2da5b0ef34dec9b7477acd00a34a3dd653ebc9d9a81442ad720a04de9f10e687", "difficulty": "medium", "final_answer": {"answer": [2.8, -8.5], "unit": "dimensionless"}, "id": "line_two_point_007898_-1.75_-0.5_2.8_-8.5", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -13.4) and (-0.5, -9.9). 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": "test", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": -0.5, "y1": -13.399999999999999, "y2": -9.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_007900(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_007900\"}", "dedupe_signature": "bb48b3926bbfd2cfb0181857b63f56c5cb18c9f741e9d2d9b0610fe0805f3519", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_007900"}, "id": "code_007900_threshold_flags_007900", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_007900(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": "test", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_007900"}, "verifier": {"function": "threshold_flags_007900", "tests": ["assert threshold_flags_007900([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_007900([], 5) == []", "assert threshold_flags_007900([-1, 0], 0) == [False, True]"], "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=64 degrees through the sine of 2 theta.\n3. Substitute v=64.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 330.0496, \"unit\": \"m\"}", "dedupe_signature": "83c5847cd0642a589926d36ad287dd67668e3125706fd877bf7c3cbd334d7f4a", "difficulty": "medium", "final_answer": {"answer": 330.0496, "unit": "m"}, "id": "projectile_range_007904_64.1_64", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 64.1 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=64.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 64, "gravity": 9.81, "speed": 64.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.34 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 428.9496, \"unit\": \"g\"}", "dedupe_signature": "920381a94d0d5ca54d0a0d9c735df8aa689e67db3e9d0fc9a34062c059327f8c", "difficulty": "medium", "final_answer": {"answer": 428.9496, "unit": "g"}, "id": "stoich_mass_007909_sodium_chloride_7.34", "license": "Apache-2.0", "prompt": "A sample contains 7.34 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.34 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.34}, "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\": [0.246, 0.634, 0.336], \"unit\": \"temperature_units\"}", "dedupe_signature": "5e0cbe0cbac76d511f5337b680c7c15e1e185e952af757f64b8a2e8428ffd36d", "difficulty": "hard", "final_answer": {"answer": [0.246, 0.634, 0.336], "unit": "temperature_units"}, "id": "heat_step_007913_0.08_2.85_-0.05_0.75_0.1_2.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.85, right=2.4; current interior values are [-0.05, 0.75, 0.1]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [-0.05, 0.75, 0.1], "left": 2.85, "r": 0.08, "right": 2.4}, "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=0.42 and add it to the current value.\nFinal: {\"answer\": [1.564, 1.161, 1.484], \"unit\": \"temperature_units\"}", "dedupe_signature": "e57efcef12e87a5b628becfda94815f4e5851f54c3fffe2032f0b39c3b896eb0", "difficulty": "hard", "final_answer": {"answer": [1.564, 1.161, 1.484], "unit": "temperature_units"}, "id": "heat_step_007931_0.42_1.25_2.95_1.35_-0.7_2.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=2.45; current interior values are [2.95, 1.35, -0.7]. 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": "test", "task_family": "finite_difference_pde", "variables": {"interior": [2.95, 1.35, -0.7], "left": 1.25, "r": 0.42, "right": 2.45}, "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=59 degrees through the sine of 2 theta.\n3. Substitute v=22.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 46.7881, \"unit\": \"m\"}", "dedupe_signature": "0ece45dbe40faacc090704f95bfad11c596fde32981a749d911bddc7fcb83d45", "difficulty": "medium", "final_answer": {"answer": 46.7881, "unit": "m"}, "id": "projectile_range_007958_22.8_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 22.8 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=22.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 22.8}, "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 slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.85, -18.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "fc89ee40f714f5998f498369a7ec8b80bd519548e97d2090f54120a66f6ee083", "difficulty": "medium", "final_answer": {"answer": [6.85, -18.5], "unit": "dimensionless"}, "id": "line_two_point_007970_6.5_16.25_6.85_-18.5", "license": "Apache-2.0", "prompt": "A line passes through points (6.5, 26.025) and (16.25, 92.8125). 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": "test", "task_family": "linear_modeling", "variables": {"x1": 6.5, "x2": 16.25, "y1": 26.025, "y2": 92.8125}, "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=0.26 and add it to the current value.\nFinal: {\"answer\": [2.018, 1.06, 0.548], \"unit\": \"temperature_units\"}", "dedupe_signature": "67e9ba90897efab78e74e32bcff1808c397f6b2f7fd2cf5a1cbcca360fb48eb0", "difficulty": "hard", "final_answer": {"answer": [2.018, 1.06, 0.548], "unit": "temperature_units"}, "id": "heat_step_007985_0.26_2.8_1.55_2.1_-1.35_2.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.8, right=2.5; current interior values are [1.55, 2.1, -1.35]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, 2.1, -1.35], "left": 2.8, "r": 0.26, "right": 2.5}, "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 = 14.75 kg and a = 14.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 207.2375, \"unit\": \"N\"}", "dedupe_signature": "098228c275b874343d869bc604dbf487416c5b9fe358d237168df891c8bc3d20", "difficulty": "easy", "final_answer": {"answer": 207.2375, "unit": "N"}, "id": "force_007992_14.75_14.05", "license": "Apache-2.0", "prompt": "A cart has mass 14.75 kg and measured acceleration 14.05 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 = 14.75 kg and a = 14.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.05, "mass": 14.75}, "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: 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": "35e631a9a56b79e5d27817566cac9861538b9652b9b445cb68e5d3033a3a83c7", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_008009_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 4532 items and budget 21255, 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": "test", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.25 kg and a = 0.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 14.175, \"unit\": \"N\"}", "dedupe_signature": "1319ffb3df9fd4ffc906affaf47e24e62243edf7e40d53c1d64559ce0b9396b1", "difficulty": "easy", "final_answer": {"answer": 14.175, "unit": "N"}, "id": "force_008010_20.25_0.7", "license": "Apache-2.0", "prompt": "A cart has mass 20.25 kg and measured acceleration 0.7 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 = 20.25 kg and a = 0.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.7, "mass": 20.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.51 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 452.1916, \"unit\": \"g\"}", "dedupe_signature": "ae7186aab5a87f152d94cd6cd5e558ce0bc0716c27af20bc65a18349c048911b", "difficulty": "medium", "final_answer": {"answer": 452.1916, "unit": "g"}, "id": "stoich_mass_008017_glucose_2.51", "license": "Apache-2.0", "prompt": "A sample contains 2.51 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.51 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 450 mL to 0.45 L.\n3. Compute M = 2.61 / 0.45.\nFinal: {\"answer\": 5.8, \"unit\": \"mol/L\"}", "dedupe_signature": "f3404fa6326beec820bc849582f8acecde0eaa755c56630a4847574251213461", "difficulty": "medium", "final_answer": {"answer": 5.8, "unit": "mol/L"}, "id": "molarity_008018_2.61_450", "license": "Apache-2.0", "prompt": "A solution contains 2.61 mol of solute in 450 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 450 mL to 0.45 L.\nCompute M = 2.61 / 0.45.", "source": "programmatic_synthetic_verified", "split": "test", "task_family": "chemistry_solutions", "variables": {"moles": 2.61, "volume_ml": 450}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}