category stringclasses 1
value | completion stringlengths 159 604 | dedupe_signature stringlengths 64 64 | difficulty stringclasses 3
values | final_answer unknown | id stringlengths 15 54 | license stringclasses 1
value | prompt stringlengths 58 241 | reasoning_trace stringlengths 101 254 | source stringclasses 1
value | split stringclasses 1
value | task_family stringclasses 16
values | variables unknown | verifier unknown |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
science_math_code | Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": -24.0132, "unit": "state_units"} | c1bf599555693416d29e448a3fc098b3edd241e93275b6ba69ca4e862f53316a | medium | {
"answer": -24.0132,
"unit": "state_units"
} | euler_decay_000261_59.5_0.94_1.85_3 | Apache-2.0 | Use explicit Euler on dy/dt = -0.94 y with y(0)=59.5, step size h=1.85, for 3 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.
Apply that update for 3 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 59.5,
"rate": 0.9400000000000001,
"step": 1.85,
"steps": 3
} | {
"tolerance": 0.0001,
"type": "euler_decay"
} |
science_math_code | Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4)=29.7 and f(8.1)=56.35.
3. The interval width is 4.1.
Final: {"answer": 176.4025, "unit": "area_units"} | a16cff3faafbc213a32b73f8bc94d843b2b00c588466ced0f6e7bd04afd3ec94 | medium | {
"answer": 176.4025,
"unit": "area_units"
} | trapz_linear_000262_6.5_3.7_4_8.1 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=6.5x+3.7 from x=4 to x=8.1. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4)=29.7 and f(8.1)=56.35.
The interval width is 4.1. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": 3.7,
"slope": 6.5,
"x0": 4,
"x1": 8.1
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [0.76, 0.62, 0.776], "unit": "temperature_units"} | 0e514c1fdf51d51512212ee9ab44fe0f81098cf7b97dacc0627b6bc0bc4ee357 | hard | {
"answer": [
0.76,
0.62,
0.776
],
"unit": "temperature_units"
} | heat_step_000263_0.34_-0.05_1.95_0.45_-0.55_2.35 | Apache-2.0 | For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.05, right=2.35; current interior values are [1.95, 0.45, -0.55]. Use r=0.34. Return the next interior vector. | Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.34 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
1.9500000000000002,
0.45,
-0.55
],
"left": -0.05,
"r": 0.34,
"right": 2.35
} | {
"tolerance": 0.0001,
"type": "heat_step"
} |
science_math_code | Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3459.5 / 100.
Final: {"answer": 34.595, "unit": "m"} | 20c16f8b5ccb0912959d71a78c9e45b76912fdbe1a044ff4feafdfc9408f6143 | easy | {
"answer": 34.595,
"unit": "m"
} | unit_convert_000264_cm_to_m_3459.5 | Apache-2.0 | Convert 3459.5 cm to m. Return the converted value with unit. | There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 3459.5 / 100. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 3459.5
} | {
"formula": "value / 100",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.3, -3.5], "unit": "dimensionless"} | e2f080f851f2c08fa2cd50c11737b49e3f7c27bde083eb57c0e87e358acc07ab | medium | {
"answer": [
-8.3,
-3.5
],
"unit": "dimensionless"
} | line_two_point_000266_-2.25_3.75_-8.3_-3.5 | Apache-2.0 | A line passes through points (-2.25, 15.175) and (3.75, -34.625). Return [slope, intercept] for y = slope*x + intercept. | The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order. | programmatic_synthetic_verified | train | linear_modeling | {
"x1": -2.25,
"x2": 3.75,
"y1": 15.175,
"y2": -34.625
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"} | 68b1c695848f010a68f4726fa6f59731f724ccf16a6e9bad453050de71876c3d | medium | {
"answer": "inconsistent"
} | dimensional_000267_inconsistent_1e14b074_27109 | Apache-2.0 | In model card equation case 27109, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason. | Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions. | programmatic_synthetic_verified | train | dimensional_analysis | {
"answer": "inconsistent",
"equation": "E = m * v"
} | {
"type": "exact"
} |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missi... | a9af82b23820eefd4a7d02e9a8a26e9da72c36a8741e9afa8af4c32c88990b4f | medium | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"required_fields",
"allowed_transformations"
]
} | abstain_000269_required_fields_allowed_transformations | Apache-2.0 | Write a sanitizer for valid billing invoice records in release 979709, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: required_fields, allowed_transformations.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | code_abstention | {
"missing": [
"required_fields",
"allowed_transformations"
]
} | {
"missing": [
"required_fields",
"allowed_transformations"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.95 kg and a = 11.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 194.0775, "unit": "N"} | 44a8ed844a1c50a1514b25cd3b1be98307b1ab86a0ae357fb8c65cc860dc3276 | easy | {
"answer": 194.0775,
"unit": "N"
} | force_000270_16.95_11.45 | Apache-2.0 | A cart has mass 16.95 kg and measured acceleration 11.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 16.95 kg and a = 11.45 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 11.45,
"mass": 16.95
} | {
"formula": "mass * acceleration",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 25.1^2 and multiply by 0.5 * 29.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9418.6495, "unit": "J"} | a2f4e7306604259d07b659ffb744b586146ec658854a487f35a768fcb4ebf758 | easy | {
"answer": 9418.6495,
"unit": "J"
} | ke_000271_29.9_25.1 | Apache-2.0 | A body of mass 29.9 kg moves at 25.1 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.1^2 and multiply by 0.5 * 29.9.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 29.9,
"velocity": 25.1
} | {
"formula": "0.5 * mass * velocity ** 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=71 degrees through the sine of 2 theta.
3. Substitute v=61.6 m/s and g=9.81 m/s^2.
Final: {"answer": 238.1411, "unit": "m"} | c7d7b30d6c48914deaa05da07ba7686a77b6b34ea856a24a36d400496198d47c | medium | {
"answer": 238.1411,
"unit": "m"
} | projectile_range_000272_61.6_71 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 61.6 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=61.6 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 71,
"gravity": 9.81,
"speed": 61.6
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.51 * 8.314 * 392 / 111.5.
Final: {"answer": 14.907, "unit": "kPa"} | 0e57be11450e9439439e3fc1e1a994cb5ead5e7d89e8e0b3dd57c374fd7dcf48 | medium | {
"answer": 14.907,
"unit": "kPa"
} | ideal_gas_000273_0.51_392_111.5 | Apache-2.0 | An ideal gas sample has n=0.51 mol, T=392 K, and V=111.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.51 * 8.314 * 392 / 111.5. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 0.51,
"temp_k": 392,
"volume_l": 111.5
} | {
"formula": "n_mol * 8.314 * temp_k / volume_l",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1300 * 0.565 * 95.
Final: {"answer": 69777.5, "unit": "J"} | 27dd9abe467339d9b2ebe09cbc269cb7613ff88f7b466ffe7b34dcff87a23ddd | easy | {
"answer": 69777.5,
"unit": "J"
} | heat_q_000274_1300_0.565_95 | Apache-2.0 | A 1300 g sample has specific heat 0.565 J/(g*K). How much heat is needed to raise its temperature by 95 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1300 * 0.565 * 95. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 95,
"heat_capacity": 0.5650000000000001,
"mass_g": 1300
} | {
"formula": "mass_g * heat_capacity * delta_t",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=128.2 V and R=44.7 ohm.
Final: {"answer": 367.6787, "unit": "W"} | a8916eba66cae4474eef4f20377d720ef43930350d6640e4bed94571fc535030 | easy | {
"answer": 367.6787,
"unit": "W"
} | ohm_power_000275_128.2_44.7 | Apache-2.0 | A resistor has resistance 44.7 ohm and voltage 128.2 V across it. Compute the dissipated power in watts. | Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=128.2 V and R=44.7 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 44.7,
"voltage": 128.2
} | {
"formula": "voltage ** 2 / resistance",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=108 mg, t=356.5 h, and T_half=18.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0002, "unit": "mg"} | ad3a8d8bb752377a6c6c50d7a223dc0c3e43d3b59bb943343597120ef5e67942 | medium | {
"answer": 0.0002,
"unit": "mg"
} | half_life_000276_108_18.5_356.5 | Apache-2.0 | A radioactive sample starts with 108 mg. Its half-life is 18.5 hours. How many mg remain after 356.5 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=108 mg, t=356.5 h, and T_half=18.5 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 356.5,
"half_life": 18.5,
"initial_amount": 108
} | {
"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.81 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 167.6781, "unit": "g"} | 2b1f6fbd44371a4b7ed43a030bfe0a1b5e24d2d5578d4a44dda58f9a00cd95cb | medium | {
"answer": 167.6781,
"unit": "g"
} | stoich_mass_000277_carbon_dioxide_3.81 | Apache-2.0 | A sample contains 3.81 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 3.81 mol * 44.01 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "carbon dioxide",
"molar_mass": 44.01,
"moles": 3.81
} | {
"formula": "moles * molar_mass",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 235 mL to 0.235 L.
3. Compute M = 0.06 / 0.235.
Final: {"answer": 0.2553, "unit": "mol/L"} | 94f60e85043a1609020297f696a5bdf4cfb89a1b67cd4b729f90b73b17870e90 | medium | {
"answer": 0.2553,
"unit": "mol/L"
} | molarity_000278_0.06_235 | Apache-2.0 | A solution contains 0.06 mol of solute in 235 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 235 mL to 0.235 L.
Compute M = 0.06 / 0.235. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 0.06,
"volume_ml": 235
} | {
"formula": "moles / (volume_ml / 1000)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.5891, "unit": "state_units"} | 314587d8c13c092fce2f01d9c7765fedab8c70430903a2c874e2926f39011c76 | medium | {
"answer": 0.5891000000000001,
"unit": "state_units"
} | euler_decay_000279_3.5_0.69_0.2_12 | Apache-2.0 | Use explicit Euler on dy/dt = -0.69 y with y(0)=3.5, step size h=0.2, for 12 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.
Apply that update for 12 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 3.5,
"rate": 0.6900000000000001,
"step": 0.2,
"steps": 12
} | {
"tolerance": 0.0001,
"type": "euler_decay"
} |
science_math_code | Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.7)=-9.75 and f(-4.9)=-2.55.
3. The interval width is 4.8.
Final: {"answer": -29.52, "unit": "area_units"} | 8173078aef6b0063d1111a94f49594e27f56cab2abe60f7b876907b4b67de604 | medium | {
"answer": -29.52,
"unit": "area_units"
} | trapz_linear_000280_1.5_4.8_-9.7_-4.9 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+4.8 from x=-9.7 to x=-4.9. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.7)=-9.75 and f(-4.9)=-2.55.
The interval width is 4.8. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": 4.8,
"slope": 1.5,
"x0": -9.7,
"x1": -4.9
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.36 and add it to the current value.
Final: {"answer": [0.148, 0.614, 0.566], "unit": "temperature_units"} | 70157f8fd3ad26d5c91ac6ae2d0526d9cf95de14f68c4e937c889ca1f7656899 | hard | {
"answer": [
0.148,
0.614,
0.5660000000000001
],
"unit": "temperature_units"
} | heat_step_000281_0.36_-1.6_1.75_0.65_-0.55_1.35 | Apache-2.0 | For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.6, right=1.35; current interior values are [1.75, 0.65, -0.55]. Use r=0.36. Return the next interior vector. | Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.36 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
1.75,
0.65,
-0.55
],
"left": -1.6,
"r": 0.36,
"right": 1.35
} | {
"tolerance": 0.0001,
"type": "heat_step"
} |
science_math_code | Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 664.0 / 100.
Final: {"answer": 6.64, "unit": "m"} | b203a68a598cbb0787580df6160a2b7b1e68604f561f0db3afef591074be5152 | easy | {
"answer": 6.64,
"unit": "m"
} | unit_convert_000282_cm_to_m_664 | Apache-2.0 | Convert 664 cm to m. Return the converted value with unit. | There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 664.0 / 100. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 664
} | {
"formula": "value / 100",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.45, -2.25], "unit": "dimensionless"} | 2855d0543be7b702c152a057d04f9d6f1d407aee6be4519f2e8014a2bfa8278f | medium | {
"answer": [
-5.45,
-2.25
],
"unit": "dimensionless"
} | line_two_point_000284_-20_-11_-5.45_-2.25 | Apache-2.0 | A line passes through points (-20, 106.75) and (-11, 57.7). Return [slope, intercept] for y = slope*x + intercept. | The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order. | programmatic_synthetic_verified | train | linear_modeling | {
"x1": -20,
"x2": -11,
"y1": 106.75,
"y2": 57.7
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.
```python
def weighted_sum_000286(values, weights):
if len(values) != len(weights):
raise ValueError('length mismatch')
return sum(value * wei... | 11224e676c4491ceab176d382d0c6217c1eca0e670eff4c1175a745665c4b511 | medium | {
"answer": "python_code",
"function": "weighted_sum_000286"
} | code_000286_weighted_sum_000286 | Apache-2.0 | Write a Python function weighted_sum_000286(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block. | Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs. | programmatic_synthetic_verified | train | python_code_generation | {
"function": "weighted_sum_000286"
} | {
"function": "weighted_sum_000286",
"tests": [
"assert weighted_sum_000286([2, 3], [4, 5]) == 23",
"assert weighted_sum_000286([], []) == 0",
"try:\n weighted_sum_000286([1], [1, 2])\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass"
],
"type": "python_tests"
} |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rat... | bdb3e984bd96b785784682b72f3463e8fd29df8a7afe7abb1f791c4515e97c7f | hard | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"rate_constant",
"number_of_steps"
]
} | abstain_000287_rate_constant_number_of_steps | Apache-2.0 | Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=20.5 and h=0.15, but omits both k and the number of steps. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | scientific_abstention | {
"missing": [
"rate_constant",
"number_of_steps"
]
} | {
"missing": [
"rate_constant",
"number_of_steps"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.6 kg and a = 4.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 62.78, "unit": "N"} | 09900152f8e120753bc1ffc7a7ef8517425599db0f6c58198371653c5050e95e | easy | {
"answer": 62.78,
"unit": "N"
} | force_000288_14.6_4.3 | Apache-2.0 | A cart has mass 14.6 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 14.6 kg and a = 4.3 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 4.3,
"mass": 14.6
} | {
"formula": "mass * acceleration",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.34 * 8.314 * 412 / 96.8.
Final: {"answer": 82.8033, "unit": "kPa"} | 1299a7d2c179a6f23c46ab002be5b887557531b947000362ff1bd635f33b543a | medium | {
"answer": 82.8033,
"unit": "kPa"
} | ideal_gas_000291_2.34_412_96.8 | Apache-2.0 | An ideal gas sample has n=2.34 mol, T=412 K, and V=96.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.34 * 8.314 * 412 / 96.8. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 2.34,
"temp_k": 412,
"volume_l": 96.8
} | {
"formula": "n_mol * 8.314 * temp_k / volume_l",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1490 * 1.8 * 6.
Final: {"answer": 16092.0, "unit": "J"} | de68067aca428372405391ffefbb444df99263a152ee7b872b6e98bf07771f1c | easy | {
"answer": 16092,
"unit": "J"
} | heat_q_000292_1490_1.8_6 | Apache-2.0 | A 1490 g sample has specific heat 1.8 J/(g*K). How much heat is needed to raise its temperature by 6 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1490 * 1.8 * 6. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 6,
"heat_capacity": 1.8,
"mass_g": 1490
} | {
"formula": "mass_g * heat_capacity * delta_t",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=71.7 V and R=112.6 ohm.
Final: {"answer": 45.6562, "unit": "W"} | 76e88f290a4ecd4b0e8121c7f8a5e79dd54f95eccb6062d73b98aac349bd3b04 | easy | {
"answer": 45.6562,
"unit": "W"
} | ohm_power_000293_71.7_112.6 | Apache-2.0 | A resistor has resistance 112.6 ohm and voltage 71.7 V across it. Compute the dissipated power in watts. | Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=71.7 V and R=112.6 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 112.6,
"voltage": 71.7
} | {
"formula": "voltage ** 2 / resistance",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=304.5 mg, t=150.5 h, and T_half=60 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 53.5185, "unit": "mg"} | f28594c6ef54b2fcfe1605a3414b69b22c5ec2f44fb65af902ab0cdcfabf6798 | medium | {
"answer": 53.5185,
"unit": "mg"
} | half_life_000294_304.5_60_150.5 | Apache-2.0 | A radioactive sample starts with 304.5 mg. Its half-life is 60 hours. How many mg remain after 150.5 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=304.5 mg, t=150.5 h, and T_half=60 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 150.5,
"half_life": 60,
"initial_amount": 304.5
} | {
"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.86 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 301.9086, "unit": "g"} | 1aebb711a7aee5f910e646bd272755b0ebe6dddcb07f6d35791b9c2969928249 | medium | {
"answer": 301.9086,
"unit": "g"
} | stoich_mass_000295_carbon_dioxide_6.86 | Apache-2.0 | A sample contains 6.86 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 6.86 mol * 44.01 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "carbon dioxide",
"molar_mass": 44.01,
"moles": 6.86
} | {
"formula": "moles * molar_mass",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.9047, "unit": "state_units"} | da47813906703e5ae9669e4f62b868b1aa5dc194abe83aeb517582e69b68c745 | medium | {
"answer": 0.9047000000000001,
"unit": "state_units"
} | euler_decay_000297_24.5_0.58_1.15_3 | Apache-2.0 | Use explicit Euler on dy/dt = -0.58 y with y(0)=24.5, step size h=1.15, for 3 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
Apply that update for 3 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 24.5,
"rate": 0.58,
"step": 1.15,
"steps": 3
} | {
"tolerance": 0.0001,
"type": "euler_decay"
} |
science_math_code | Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.2)=-43.44 and f(3.5)=14.85.
3. The interval width is 8.7.
Final: {"answer": -124.3665, "unit": "area_units"} | 4ca4a00febaec0d9a30c38a20033fcaccf0c64e1d9e9dbc2b9c6561e13f92a09 | medium | {
"answer": -124.3665,
"unit": "area_units"
} | trapz_linear_000298_6.7_-8.6_-5.2_3.5 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+-8.6 from x=-5.2 to x=3.5. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.2)=-43.44 and f(3.5)=14.85.
The interval width is 8.7. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": -8.6,
"slope": 6.7,
"x0": -5.2,
"x1": 3.5
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.3 and add it to the current value.
Final: {"answer": [0.09, 0.505, 0.715], "unit": "temperature_units"} | fc95290dec6491fe7735c60a5e0ee50ffb29fbfdf5703b97e29a2f5949e4be15 | hard | {
"answer": [
0.09,
0.505,
0.715
],
"unit": "temperature_units"
} | heat_step_000299_0.3_-1.5_1.05_0.4_0.1_1.85 | Apache-2.0 | For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.5, right=1.85; current interior values are [1.05, 0.4, 0.1]. Use r=0.3. Return the next interior vector. | Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.3 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
1.05,
0.4,
0.1
],
"left": -1.5,
"r": 0.30000000000000004,
"right": 1.85
} | {
"tolerance": 0.0001,
"type": "heat_step"
} |
science_math_code | Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22119.0 / 1000.
Final: {"answer": 22.119, "unit": "kg"} | d610c1b420339f608f1cff4e6ba5752301d4736373c83b30b5ad4865c31eba55 | easy | {
"answer": 22.119,
"unit": "kg"
} | unit_convert_000300_g_to_kg_22119 | Apache-2.0 | Convert 22119 g to kg. Return the converted value with unit. | There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 22119.0 / 1000. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 22119
} | {
"formula": "value / 1000",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=148 degrees and keep the unit as newtons.
Final: {"answer": [-355.7562, 222.3011], "unit": "N"} | 7f62974b44c12275e3bd4c0669f524aacf298f58fcd5988e731bb88de244f046 | medium | {
"answer": [
-355.7562,
222.3011
],
"unit": "N"
} | vector_components_000301_419.5_148 | Apache-2.0 | A vector has magnitude 419.5 N at 148 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons. | The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=148 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 148,
"magnitude": 419.5
} | {
"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.8, -24.75], "unit": "dimensionless"} | 93fae5eadc6d47160a0b7a700d7f730df1280b305445a8db4b06d13351d6e5b4 | medium | {
"answer": [
8.8,
-24.75
],
"unit": "dimensionless"
} | line_two_point_000302_-7.25_-4.5_8.8_-24.75 | Apache-2.0 | A line passes through points (-7.25, -88.55) and (-4.5, -64.35). Return [slope, intercept] for y = slope*x + intercept. | The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order. | programmatic_synthetic_verified | train | linear_modeling | {
"x1": -7.25,
"x2": -4.5,
"y1": -88.55,
"y2": -64.35
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Compare the dimensions on both sides of the equation.
2. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"} | d4516bded55045431e507d612c94b439f807d88e9eaa7d558d6210d2ac8765b9 | medium | {
"answer": "inconsistent"
} | dimensional_000303_inconsistent_c1271127_655693 | Apache-2.0 | In quality-control check case 655693, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason. | Compare the dimensions on both sides of the equation.
velocity divided by time is acceleration
The equation is valid only if both sides have identical dimensions. | programmatic_synthetic_verified | train | dimensional_analysis | {
"answer": "inconsistent",
"equation": "x = v / t"
} | {
"type": "exact"
} |
science_math_code | Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.
```python
def pairwise_ratios_000304(numerators, denominators):
if len(numerators) != len(denominators):
raise ValueError('length mismatch')
o... | 26999618391a309cc3180c2b4c47cddf330794b3fa67c05ef3d446d675546c4b | medium | {
"answer": "python_code",
"function": "pairwise_ratios_000304"
} | code_000304_pairwise_ratios_000304 | Apache-2.0 | Write a Python function pairwise_ratios_000304(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block. | Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs. | programmatic_synthetic_verified | train | python_code_generation | {
"function": "pairwise_ratios_000304"
} | {
"function": "pairwise_ratios_000304",
"tests": [
"assert pairwise_ratios_000304([2, 9], [4, 3]) == [0.5, 3.0]",
"try:\n pairwise_ratios_000304([1], [0])\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass",
"try:\n pairwise_ratios_000304([1, 2], [1])\n raise Asserti... |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]} | f3b9969591b1dafb20ef16522409679205efd7f36277092c0192a4e9def07afa | medium | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"volume"
]
} | abstain_000305_volume | Apache-2.0 | Compute pressure from the ideal gas law. The prompt gives n=5.97 mol and T=347 K, but does not give volume. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: volume.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | scientific_abstention | {
"missing": [
"volume"
]
} | {
"missing": [
"volume"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 10.6^2 and multiply by 0.5 * 20.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1160.117, "unit": "J"} | 898e47eef75294882bafa0db71c8b9c4953462449842e904f93477c352704a57 | easy | {
"answer": 1160.117,
"unit": "J"
} | ke_000307_20.65_10.6 | Apache-2.0 | A body of mass 20.65 kg moves at 10.6 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.6^2 and multiply by 0.5 * 20.65.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 20.65,
"velocity": 10.6
} | {
"formula": "0.5 * mass * velocity ** 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=59 degrees through the sine of 2 theta.
3. Substitute v=28.5 m/s and g=9.81 m/s^2.
Final: {"answer": 73.1064, "unit": "m"} | 8162b0d047de2341ee03da4849812899a585c761ec4d318292e19cf01c83dbcf | medium | {
"answer": 73.1064,
"unit": "m"
} | projectile_range_000308_28.5_59 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 28.5 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=59 degrees through the sine of 2 theta.
Substitute v=28.5 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 59,
"gravity": 9.81,
"speed": 28.5
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.9 * 8.314 * 444 / 74.5.
Final: {"answer": 292.3403, "unit": "kPa"} | e84bae30fe3c2fef0525159ca67ac76bc74161dada568355d1d4cabb1902f617 | medium | {
"answer": 292.3403,
"unit": "kPa"
} | ideal_gas_000309_5.9_444_74.5 | Apache-2.0 | An ideal gas sample has n=5.9 mol, T=444 K, and V=74.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.9 * 8.314 * 444 / 74.5. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 5.9,
"temp_k": 444,
"volume_l": 74.5
} | {
"formula": "n_mol * 8.314 * temp_k / volume_l",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 455 * 4.665 * 74.
Final: {"answer": 157070.55, "unit": "J"} | 25dbb5629dc6c2d2f46663eb30678542f3d6ab64931c4ea0b6b05875ff494bc1 | easy | {
"answer": 157070.55,
"unit": "J"
} | heat_q_000310_455_4.665_74 | Apache-2.0 | A 455 g sample has specific heat 4.665 J/(g*K). How much heat is needed to raise its temperature by 74 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 455 * 4.665 * 74. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 74,
"heat_capacity": 4.665,
"mass_g": 455
} | {
"formula": "mass_g * heat_capacity * delta_t",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=50.7 V and R=150.1 ohm.
Final: {"answer": 17.1252, "unit": "W"} | 21a712d3493853496414e8fc131249fcb691d8d17bf1ccbfa9208392bf4a17b7 | easy | {
"answer": 17.1252,
"unit": "W"
} | ohm_power_000311_50.7_150.1 | Apache-2.0 | A resistor has resistance 150.1 ohm and voltage 50.7 V across it. Compute the dissipated power in watts. | Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=50.7 V and R=150.1 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 150.1,
"voltage": 50.7
} | {
"formula": "voltage ** 2 / resistance",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=240.5 mg, t=10.5 h, and T_half=78 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 219.0745, "unit": "mg"} | 2ba0a4398d152daae1d332aef5ed7186f0d853460c864cebcf9471931185f173 | medium | {
"answer": 219.0745,
"unit": "mg"
} | half_life_000312_240.5_78_10.5 | Apache-2.0 | A radioactive sample starts with 240.5 mg. Its half-life is 78 hours. How many mg remain after 10.5 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=240.5 mg, t=10.5 h, and T_half=78 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 10.5,
"half_life": 78,
"initial_amount": 240.5
} | {
"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.21 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 578.3008, "unit": "g"} | ceaeff9bdf0f495a8c41f348437a8465e356f8b76ae7fd031f2583993d5b4393 | medium | {
"answer": 578.3008,
"unit": "g"
} | stoich_mass_000313_glucose_3.21 | Apache-2.0 | A sample contains 3.21 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 3.21 mol * 180.156 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "glucose",
"molar_mass": 180.156,
"moles": 3.21
} | {
"formula": "moles * molar_mass",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1375 mL to 1.375 L.
3. Compute M = 2.05 / 1.375.
Final: {"answer": 1.4909, "unit": "mol/L"} | 8db87578d59b364f2459a71aab5b5248d51adeef996e776fc6640ea78fcc0996 | medium | {
"answer": 1.4909,
"unit": "mol/L"
} | molarity_000314_2.05_1375 | Apache-2.0 | A solution contains 2.05 mol of solute in 1375 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 1375 mL to 1.375 L.
Compute M = 2.05 / 1.375. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 2.05,
"volume_ml": 1375
} | {
"formula": "moles / (volume_ml / 1000)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.4)=34.14 and f(8.3)=56.68.
3. The interval width is 4.9.
Final: {"answer": 222.509, "unit": "area_units"} | fb70279924cd22f9caeb9daa9841cb7e96b8fa94299d8f18c3208ff3afb4761c | medium | {
"answer": 222.509,
"unit": "area_units"
} | trapz_linear_000316_4.6_18.5_3.4_8.3 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=4.6x+18.5 from x=3.4 to x=8.3. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.4)=34.14 and f(8.3)=56.68.
The interval width is 4.9. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": 18.5,
"slope": 4.6,
"x0": 3.4,
"x1": 8.3
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [-0.827, -1.509, -0.784], "unit": "temperature_units"} | 0c6ac27e8134931e232df4c79742685a26747e1f339243a8ea9f9440720a492b | hard | {
"answer": [
-0.8270000000000001,
-1.509,
-0.784
],
"unit": "temperature_units"
} | heat_step_000317_0.22_2.8_-1.85_-1.85_-0.3_-0.95 | Apache-2.0 | For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.8, right=-0.95; current interior values are [-1.85, -1.85, -0.3]. Use r=0.22. Return the next interior vector. | Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.22 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
-1.85,
-1.85,
-0.30000000000000004
],
"left": 2.8,
"r": 0.22,
"right": -0.9500000000000001
} | {
"tolerance": 0.0001,
"type": "heat_step"
} |
science_math_code | Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=292 degrees and keep the unit as newtons.
Final: {"answer": [51.3211, -127.0242], "unit": "N"} | 12849e9920404ceeb2e58a84835137020a778a62084284dc0ee1525a72a39261 | medium | {
"answer": [
51.3211,
-127.0242
],
"unit": "N"
} | vector_components_000319_137_292 | Apache-2.0 | A vector has magnitude 137 N at 292 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons. | The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=292 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 292,
"magnitude": 137
} | {
"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.5, 23.75], "unit": "dimensionless"} | c1f1fd1de1859eed5cb219093316855b03fadb09629e1267c0ca45fc796e0e12 | medium | {
"answer": [
-9.5,
23.75
],
"unit": "dimensionless"
} | line_two_point_000320_4.75_17.75_-9.5_23.75 | Apache-2.0 | A line passes through points (4.75, -21.375) and (17.75, -144.875). Return [slope, intercept] for y = slope*x + intercept. | The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order. | programmatic_synthetic_verified | train | linear_modeling | {
"x1": 4.75,
"x2": 17.75,
"y1": -21.375,
"y2": -144.875
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.
```python
def center_values_000322(values):
if not values:
raise ValueError('center_values requires at least one value')
mean = sum(values) / ... | fc57360a82d9cc2eb78ded053ec5fa5106547c6e286672c96566e84c16976a63 | medium | {
"answer": "python_code",
"function": "center_values_000322"
} | code_000322_center_values_000322 | Apache-2.0 | Write a Python function center_values_000322(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block. | Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs. | programmatic_synthetic_verified | train | python_code_generation | {
"function": "center_values_000322"
} | {
"function": "center_values_000322",
"tests": [
"out = center_values_000322([1, 2, 3]); assert out == [-1, 0, 1]",
"assert center_values_000322([5]) == [0]",
"try:\n center_values_000322([])\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass"
],
"type": "python_tests"... |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rat... | 4406a66f13219f415e07a85cb7ceba3d5a0fa42e6878f49a15afdf6bf72386e3 | hard | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"rate_constant",
"number_of_steps"
]
} | abstain_000323_rate_constant_number_of_steps | Apache-2.0 | Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=23.5 and h=0.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | scientific_abstention | {
"missing": [
"rate_constant",
"number_of_steps"
]
} | {
"missing": [
"rate_constant",
"number_of_steps"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 4.3^2 and multiply by 0.5 * 21.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 202.4655, "unit": "J"} | 46ed047ffa2ab982847c03eac507c6698d12f11ae9842cc8300efe97b7627fcd | easy | {
"answer": 202.4655,
"unit": "J"
} | ke_000325_21.9_4.3 | Apache-2.0 | A body of mass 21.9 kg moves at 4.3 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 4.3^2 and multiply by 0.5 * 21.9.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 21.9,
"velocity": 4.3
} | {
"formula": "0.5 * mass * velocity ** 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=80 degrees through the sine of 2 theta.
3. Substitute v=49.6 m/s and g=9.81 m/s^2.
Final: {"answer": 85.7721, "unit": "m"} | a2dafce3659fb360973480accbb07f92a4105cf803c82aaf89654e310c746581 | medium | {
"answer": 85.7721,
"unit": "m"
} | projectile_range_000326_49.6_80 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 49.6 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=80 degrees through the sine of 2 theta.
Substitute v=49.6 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 80,
"gravity": 9.81,
"speed": 49.6
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.52 * 8.314 * 379 / 118.1.
Final: {"answer": 13.874, "unit": "kPa"} | f4d7c22b2decc8e59a22051ea054035701ad93d061b0736d256288d4c5f08b6a | medium | {
"answer": 13.874,
"unit": "kPa"
} | ideal_gas_000327_0.52_379_118.1 | Apache-2.0 | An ideal gas sample has n=0.52 mol, T=379 K, and V=118.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.52 * 8.314 * 379 / 118.1. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 0.52,
"temp_k": 379,
"volume_l": 118.1
} | {
"formula": "n_mol * 8.314 * temp_k / volume_l",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1700 * 1.245 * 63.
Final: {"answer": 133339.5, "unit": "J"} | a0292873ff2332d24de906992159b090608b6d217dd07425349285066a7215b3 | easy | {
"answer": 133339.5,
"unit": "J"
} | heat_q_000328_1700_1.245_63 | Apache-2.0 | A 1700 g sample has specific heat 1.245 J/(g*K). How much heat is needed to raise its temperature by 63 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1700 * 1.245 * 63. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 63,
"heat_capacity": 1.245,
"mass_g": 1700
} | {
"formula": "mass_g * heat_capacity * delta_t",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=294.5 mg, t=52 h, and T_half=16 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 30.9555, "unit": "mg"} | bc6680bff7a4f956e4e864295943bc52907228fb647e3395dc5581b33411ab59 | medium | {
"answer": 30.9555,
"unit": "mg"
} | half_life_000330_294.5_16_52 | Apache-2.0 | A radioactive sample starts with 294.5 mg. Its half-life is 16 hours. How many mg remain after 52 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=294.5 mg, t=52 h, and T_half=16 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 52,
"half_life": 16,
"initial_amount": 294.5
} | {
"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.69 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 102.5054, "unit": "g"} | 55ccafe8c3d3b0f4cb5c01c8dfee083aeb4bde7d1440abc654b858ab5a8c32e8 | medium | {
"answer": 102.5054,
"unit": "g"
} | stoich_mass_000331_water_5.69 | Apache-2.0 | A sample contains 5.69 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 5.69 mol * 18.015 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "water",
"molar_mass": 18.015,
"moles": 5.69
} | {
"formula": "moles * molar_mass",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3410 mL to 3.41 L.
3. Compute M = 3.07 / 3.41.
Final: {"answer": 0.9003, "unit": "mol/L"} | 51db641711641af9922855660b7a3cdb6a616889e3198c1ccb4ce51ae71c97c6 | medium | {
"answer": 0.9003,
"unit": "mol/L"
} | molarity_000332_3.07_3410 | Apache-2.0 | A solution contains 3.07 mol of solute in 3410 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 3410 mL to 3.41 L.
Compute M = 3.07 / 3.41. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 3.07,
"volume_ml": 3410
} | {
"formula": "moles / (volume_ml / 1000)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 20.7251, "unit": "state_units"} | 745164d604b244365e28d985f336b3a0e35301ae470239f16e3266b2cae72f4f | medium | {
"answer": 20.7251,
"unit": "state_units"
} | euler_decay_000333_66.5_0.81_0.15_9 | Apache-2.0 | Use explicit Euler on dy/dt = -0.81 y with y(0)=66.5, step size h=0.15, for 9 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.
Apply that update for 9 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 66.5,
"rate": 0.81,
"step": 0.15,
"steps": 9
} | {
"tolerance": 0.0001,
"type": "euler_decay"
} |
science_math_code | Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.12 and add it to the current value.
Final: {"answer": [0.648, 2.034, 0.53], "unit": "temperature_units"} | 599ef91ff373c30e95ef10672ee7efa1440aebc1473da00c93356126567a555c | hard | {
"answer": [
0.648,
2.034,
0.53
],
"unit": "temperature_units"
} | heat_step_000335_0.12_0.0_0.45_2.55_0.35_-0.35 | Apache-2.0 | For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0, right=-0.35; current interior values are [0.45, 2.55, 0.35]. Use r=0.12. Return the next interior vector. | Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.12 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
0.45,
2.55,
0.35000000000000003
],
"left": 0,
"r": 0.12,
"right": -0.35000000000000003
} | {
"tolerance": 0.0001,
"type": "heat_step"
} |
science_math_code | Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=125 degrees and keep the unit as newtons.
Final: {"answer": [-138.8055, 198.2348], "unit": "N"} | 9c5ff9aeef27406c5a84a5501d8402b0a67bd326a2dff772b5bb5674365e04ac | medium | {
"answer": [
-138.8055,
198.2348
],
"unit": "N"
} | vector_components_000337_242_125 | Apache-2.0 | A vector has magnitude 242 N at 125 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons. | The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=125 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 125,
"magnitude": 242
} | {
"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-3.4, -29.75], "unit": "dimensionless"} | 4e301fde147f50f4523e6bd2f2c3d9898027eaa7dc44d30cad01d98f26db022f | medium | {
"answer": [
-3.4,
-29.75
],
"unit": "dimensionless"
} | line_two_point_000338_-16.5_-9.5_-3.4_-29.75 | Apache-2.0 | A line passes through points (-16.5, 26.35) and (-9.5, 2.55). Return [slope, intercept] for y = slope*x + intercept. | The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order. | programmatic_synthetic_verified | train | linear_modeling | {
"x1": -16.5,
"x2": -9.5,
"y1": 26.35,
"y2": 2.55
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"} | 52df2c4e876dac03af69f7abdc724152eb9a0adcc9cab784ad0160354a5a35c0 | medium | {
"answer": "consistent"
} | dimensional_000339_consistent_8b38953d_938328 | Apache-2.0 | In student derivation case 938328, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason. | Compare the dimensions on both sides of the equation.
coulomb per second is ampere
The equation is valid only if both sides have identical dimensions. | programmatic_synthetic_verified | train | dimensional_analysis | {
"answer": "consistent",
"equation": "I = Q / t"
} | {
"type": "exact"
} |
science_math_code | Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.
```python
def normalize_000340(values):
total = sum(values)
if total == 0:
raise ValueError('cannot normalize zero-sum values')
return [v ... | 26e8d5e21c21f7147f56e14b5ea693458224c274f7d189bb686f1d9fc8d9a2a5 | medium | {
"answer": "python_code",
"function": "normalize_000340"
} | code_000340_normalize_000340 | Apache-2.0 | Write a Python function normalize_000340(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block. | Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs. | programmatic_synthetic_verified | train | python_code_generation | {
"function": "normalize_000340"
} | {
"function": "normalize_000340",
"tests": [
"out = normalize_000340([2, 3, 5]); assert len(out) == 3",
"assert abs(sum(normalize_000340([2, 3, 5])) - 1.0) < 1e-12",
"assert normalize_000340([1, 1]) == [0.5, 0.5]",
"try:\n normalize_000340([1, -1])\n raise AssertionError('expected ValueError')... |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rat... | be57d2770586f7de4e553b42f1d0ac639e9d5c9dde14fd33a922c82430d391f3 | hard | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"rate_constant",
"number_of_steps"
]
} | abstain_000341_rate_constant_number_of_steps | Apache-2.0 | Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=11.5 and h=1.65, but omits both k and the number of steps. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | scientific_abstention | {
"missing": [
"rate_constant",
"number_of_steps"
]
} | {
"missing": [
"rate_constant",
"number_of_steps"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.5 kg and a = 3.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 66.5, "unit": "N"} | 234b482539f2bf2b58aa48d6ff30f9c09f76796a09c16c08bc592ad6088e05ed | easy | {
"answer": 66.5,
"unit": "N"
} | force_000342_17.5_3.8 | Apache-2.0 | A cart has mass 17.5 kg and measured acceleration 3.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 17.5 kg and a = 3.8 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 3.8,
"mass": 17.5
} | {
"formula": "mass * acceleration",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.25^2 and multiply by 0.5 * 7.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7014.6094, "unit": "J"} | 0f4fddb55aae8a8c6a6e6ac6496266b9727eb80d14c4d516ce2533d6e11b213b | easy | {
"answer": 7014.6094,
"unit": "J"
} | ke_000343_7.5_43.25 | Apache-2.0 | A body of mass 7.5 kg moves at 43.25 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.25^2 and multiply by 0.5 * 7.5.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 7.5,
"velocity": 43.25
} | {
"formula": "0.5 * mass * velocity ** 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=56 degrees through the sine of 2 theta.
3. Substitute v=52.5 m/s and g=9.81 m/s^2.
Final: {"answer": 260.5046, "unit": "m"} | 82cf9ddf6dcef4a6d90f706217007b476def9bfeefa244cdaa2a3eb71941e2be | medium | {
"answer": 260.5046,
"unit": "m"
} | projectile_range_000344_52.5_56 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 52.5 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=56 degrees through the sine of 2 theta.
Substitute v=52.5 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 56,
"gravity": 9.81,
"speed": 52.5
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.23 * 8.314 * 602 / 50.7.
Final: {"answer": 318.8608, "unit": "kPa"} | fdcf388d9ef069f3c58fd593bbce497cf88c8f61d74a1e9ac9952549878dc674 | medium | {
"answer": 318.8608,
"unit": "kPa"
} | ideal_gas_000345_3.23_602_50.7 | Apache-2.0 | An ideal gas sample has n=3.23 mol, T=602 K, and V=50.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.23 * 8.314 * 602 / 50.7. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 3.23,
"temp_k": 602,
"volume_l": 50.7
} | {
"formula": "n_mol * 8.314 * temp_k / volume_l",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1495 * 3.77 * 90.
Final: {"answer": 507253.5, "unit": "J"} | d41bc8c0080a1eebfd543613843055d6805127d56b970753905bc016e60b5581 | easy | {
"answer": 507253.5,
"unit": "J"
} | heat_q_000346_1495_3.77_90 | Apache-2.0 | A 1495 g sample has specific heat 3.77 J/(g*K). How much heat is needed to raise its temperature by 90 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1495 * 3.77 * 90. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 90,
"heat_capacity": 3.77,
"mass_g": 1495
} | {
"formula": "mass_g * heat_capacity * delta_t",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=80.5 V and R=1.2 ohm.
Final: {"answer": 5400.2083, "unit": "W"} | 8479be912dbf656b70d651053899524b51f1b4b723b848a761fffc4e5441bfb0 | easy | {
"answer": 5400.2083,
"unit": "W"
} | ohm_power_000347_80.5_1.2 | Apache-2.0 | A resistor has resistance 1.2 ohm and voltage 80.5 V across it. Compute the dissipated power in watts. | Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=80.5 V and R=1.2 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 1.2,
"voltage": 80.5
} | {
"formula": "voltage ** 2 / resistance",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=470 mg, t=181 h, and T_half=26 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 3.7711, "unit": "mg"} | 66a3cccc4f7f29d7e2d7a7528399b9e4c9018af895004d84619f6067a96e8ce7 | medium | {
"answer": 3.7711,
"unit": "mg"
} | half_life_000348_470_26_181 | Apache-2.0 | A radioactive sample starts with 470 mg. Its half-life is 26 hours. How many mg remain after 181 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=470 mg, t=181 h, and T_half=26 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 181,
"half_life": 26,
"initial_amount": 470
} | {
"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.94 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 54.9336, "unit": "g"} | fe33c683e63e330a672e60751724b1f8d4fc6e083c049793d30a6063b6cba3f8 | medium | {
"answer": 54.9336,
"unit": "g"
} | stoich_mass_000349_sodium_chloride_0.94 | Apache-2.0 | A sample contains 0.94 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 0.94 mol * 58.44 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "sodium chloride",
"molar_mass": 58.44,
"moles": 0.9400000000000001
} | {
"formula": "moles * molar_mass",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.89 y, so each step multiplies y by 1 - h*0.89.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.2577, "unit": "state_units"} | 3b6dd56855968d3cd76289c45b1c76b9c0b79e335e9726b95da222cb5674d35a | medium | {
"answer": 0.2577,
"unit": "state_units"
} | euler_decay_000351_54_0.89_0.6_7 | Apache-2.0 | Use explicit Euler on dy/dt = -0.89 y with y(0)=54, step size h=0.6, for 7 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.89 y, so each step multiplies y by 1 - h*0.89.
Apply that update for 7 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 54,
"rate": 0.89,
"step": 0.6000000000000001,
"steps": 7
} | {
"tolerance": 0.0001,
"type": "euler_decay"
} |
science_math_code | Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.3)=-57.81 and f(10.4)=-69.78.
3. The interval width is 2.1.
Final: {"answer": -133.9695, "unit": "area_units"} | c162b815043aa29a8f74f9a9638e2cdc8e31fb7646b9218900d8351f46eace72 | medium | {
"answer": -133.9695,
"unit": "area_units"
} | trapz_linear_000352_-5.7_-10.5_8.3_10.4 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.7x+-10.5 from x=8.3 to x=10.4. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.3)=-57.81 and f(10.4)=-69.78.
The interval width is 2.1. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": -10.5,
"slope": -5.7,
"x0": 8.3,
"x1": 10.4
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [0.108, -0.118, -0.232], "unit": "temperature_units"} | 074ef7451a92c5380663f6e87bed5394cffdd0a16c73a61b31dce61faf5a68cf | hard | {
"answer": [
0.108,
-0.11800000000000001,
-0.232
],
"unit": "temperature_units"
} | heat_step_000353_0.28_2.0_-1.95_1.45_-0.75_-1.1 | Apache-2.0 | For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2, right=-1.1; current interior values are [-1.95, 1.45, -0.75]. Use r=0.28. Return the next interior vector. | Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.28 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
-1.9500000000000002,
1.45,
-0.75
],
"left": 2,
"r": 0.28,
"right": -1.1
} | {
"tolerance": 0.0001,
"type": "heat_step"
} |
science_math_code | Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=147 degrees and keep the unit as newtons.
Final: {"answer": [-288.5027, 187.3558], "unit": "N"} | d17d2d4ee99101388b81806c89173a232127092ed2cd296b9d925c81b1177742 | medium | {
"answer": [
-288.5027,
187.3558
],
"unit": "N"
} | vector_components_000355_344_147 | Apache-2.0 | A vector has magnitude 344 N at 147 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons. | The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=147 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 147,
"magnitude": 344
} | {
"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.2, 21.0], "unit": "dimensionless"} | 0fe1991cb27a8a3fb534e8b3c4dd746b7bec3c65139fda3ff67542c6a7fc53b6 | medium | {
"answer": [
-0.2,
21
],
"unit": "dimensionless"
} | line_two_point_000356_8.25_9_-0.2_21 | Apache-2.0 | A line passes through points (8.25, 19.35) and (9, 19.2). Return [slope, intercept] for y = slope*x + intercept. | The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order. | programmatic_synthetic_verified | train | linear_modeling | {
"x1": 8.25,
"x2": 9,
"y1": 19.35,
"y2": 19.2
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Compare the dimensions on both sides of the equation.
2. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"} | d0c05ec652b9a36b6f323d934376d4884e092337924a03b98317d4498838b64f | medium | {
"answer": "inconsistent"
} | dimensional_000357_inconsistent_74ac0b02_406659 | Apache-2.0 | In lab notebook case 406659, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason. | Compare the dimensions on both sides of the equation.
amount times volume is not concentration
The equation is valid only if both sides have identical dimensions. | programmatic_synthetic_verified | train | dimensional_analysis | {
"answer": "inconsistent",
"equation": "C = n * V"
} | {
"type": "exact"
} |
science_math_code | Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.
```python
def running_total_000358(values):
total = 0
out = []
for value in values:
total += value
out.append(total)
return ou... | 5be8d6360c2f8caf40ecd2ce28ade276e081905a96842c7146fbb693b8d465f0 | medium | {
"answer": "python_code",
"function": "running_total_000358"
} | code_000358_running_total_000358 | Apache-2.0 | Write a Python function running_total_000358(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block. | Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs. | programmatic_synthetic_verified | train | python_code_generation | {
"function": "running_total_000358"
} | {
"function": "running_total_000358",
"tests": [
"assert running_total_000358([1, 2, 3]) == [1, 3, 6]",
"xs = [4, -1, 2]; assert running_total_000358(xs) == [4, 3, 5] and xs == [4, -1, 2]",
"assert running_total_000358([]) == []"
],
"type": "python_tests"
} |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rat... | 201db1611441323da146a1933f637c4fc038b654cd5f0f1badb720233e5c0eed | hard | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"rate_constant",
"number_of_steps"
]
} | abstain_000359_rate_constant_number_of_steps | Apache-2.0 | Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=44 and h=0.45, but omits both k and the number of steps. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | scientific_abstention | {
"missing": [
"rate_constant",
"number_of_steps"
]
} | {
"missing": [
"rate_constant",
"number_of_steps"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 8.25 kg and a = 13.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 110.9625, "unit": "N"} | c365b84e62b8b12089ef93d04af2cda561339ec58e38969e82f831da80932342 | easy | {
"answer": 110.9625,
"unit": "N"
} | force_000360_8.25_13.45 | Apache-2.0 | A cart has mass 8.25 kg and measured acceleration 13.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 8.25 kg and a = 13.45 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 13.45,
"mass": 8.25
} | {
"formula": "mass * acceleration",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=36 degrees through the sine of 2 theta.
3. Substitute v=30.1 m/s and g=9.81 m/s^2.
Final: {"answer": 87.8355, "unit": "m"} | f36764e40761d58e59f6104e93ba6bf0d79fab3ea08fa04140cd55782e4adcd5 | medium | {
"answer": 87.8355,
"unit": "m"
} | projectile_range_000362_30.1_36 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 30.1 m/s and angle 36 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=36 degrees through the sine of 2 theta.
Substitute v=30.1 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 36,
"gravity": 9.81,
"speed": 30.1
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.01 * 8.314 * 242 / 119.0.
Final: {"answer": 84.7064, "unit": "kPa"} | 226beb823be662e3317dcc1b1dd8980f0c0fb8247eb38adfb29d35d0b2cbb5b7 | medium | {
"answer": 84.7064,
"unit": "kPa"
} | ideal_gas_000363_5.01_242_119.0 | Apache-2.0 | An ideal gas sample has n=5.01 mol, T=242 K, and V=119.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.01 * 8.314 * 242 / 119.0. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 5.01,
"temp_k": 242,
"volume_l": 119
} | {
"formula": "n_mol * 8.314 * temp_k / volume_l",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=206.5 V and R=163.4 ohm.
Final: {"answer": 260.9685, "unit": "W"} | 09af20a14ebf09cba7b66af1fb38e4ddf79c427f0c046c460954fbec8954f3c1 | easy | {
"answer": 260.9685,
"unit": "W"
} | ohm_power_000365_206.5_163.4 | Apache-2.0 | A resistor has resistance 163.4 ohm and voltage 206.5 V across it. Compute the dissipated power in watts. | Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=206.5 V and R=163.4 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 163.4,
"voltage": 206.5
} | {
"formula": "voltage ** 2 / resistance",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=326.5 mg, t=35.5 h, and T_half=77 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 237.1901, "unit": "mg"} | 2a50c457f35b928dcf65f2469042d8e0ff284da1d35b9c5ac14be845e40151b1 | medium | {
"answer": 237.1901,
"unit": "mg"
} | half_life_000366_326.5_77_35.5 | Apache-2.0 | A radioactive sample starts with 326.5 mg. Its half-life is 77 hours. How many mg remain after 35.5 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=326.5 mg, t=35.5 h, and T_half=77 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 35.5,
"half_life": 77,
"initial_amount": 326.5
} | {
"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.57 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 46.2985, "unit": "g"} | e331e9840c8811177e0dd5c93e37e5b9f8bf1942345544962e2cdb5134b8be8d | medium | {
"answer": 46.2985,
"unit": "g"
} | stoich_mass_000367_water_2.57 | Apache-2.0 | A sample contains 2.57 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 2.57 mol * 18.015 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "water",
"molar_mass": 18.015,
"moles": 2.5700000000000003
} | {
"formula": "moles * molar_mass",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2455 mL to 2.455 L.
3. Compute M = 3.795 / 2.455.
Final: {"answer": 1.5458, "unit": "mol/L"} | 642a2f1d9fe0da1b94561a61e3ed1cc0da02240b956a1eecc9a59ade3be74165 | medium | {
"answer": 1.5458,
"unit": "mol/L"
} | molarity_000368_3.795_2455 | Apache-2.0 | A solution contains 3.795 mol of solute in 2455 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 2455 mL to 2.455 L.
Compute M = 3.795 / 2.455. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 3.795,
"volume_ml": 2455
} | {
"formula": "moles / (volume_ml / 1000)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 28.2612, "unit": "state_units"} | c50bd732b3a162b1b2e7e0fe800b4459bd50fa9c5786eb5fce21aee2551cac11 | medium | {
"answer": 28.2612,
"unit": "state_units"
} | euler_decay_000369_58.5_0.64_0.1_11 | Apache-2.0 | Use explicit Euler on dy/dt = -0.64 y with y(0)=58.5, step size h=0.1, for 11 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
Apply that update for 11 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 58.5,
"rate": 0.64,
"step": 0.1,
"steps": 11
} | {
"tolerance": 0.0001,
"type": "euler_decay"
} |
science_math_code | Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.7)=19.81 and f(10.3)=44.19.
3. The interval width is 4.6.
Final: {"answer": 147.2, "unit": "area_units"} | d566675334aacd10ce2991de8b61c4cc6bed98cd7a6959aaaa1e481b8e6d0f08 | medium | {
"answer": 147.2,
"unit": "area_units"
} | trapz_linear_000370_5.3_-10.4_5.7_10.3 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=5.3x+-10.4 from x=5.7 to x=10.3. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.7)=19.81 and f(10.3)=44.19.
The interval width is 4.6. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": -10.4,
"slope": 5.3,
"x0": 5.7,
"x1": 10.3
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [1.387, 1.911, 1.344], "unit": "temperature_units"} | fd0bacdae1fa6ef027bab4b620e1d32cb0c76985a4f4f3868ead4fc739fb3f5b | hard | {
"answer": [
1.387,
1.911,
1.344
],
"unit": "temperature_units"
} | heat_step_000371_0.38_1.25_2.85_0.6_1.8_1.8 | Apache-2.0 | For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=1.8; current interior values are [2.85, 0.6, 1.8]. Use r=0.38. Return the next interior vector. | Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.38 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
2.85,
0.6000000000000001,
1.8
],
"left": 1.25,
"r": 0.38,
"right": 1.8
} | {
"tolerance": 0.0001,
"type": "heat_step"
} |
science_math_code | Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 212.5 + 273.15.
Final: {"answer": 485.65, "unit": "K"} | 41a4a5aa5bd4b09604a54484d5bd3ff338f2099d199147ceea58c0f7fe0b652b | easy | {
"answer": 485.65,
"unit": "K"
} | unit_convert_000372_c_to_k_212.5 | Apache-2.0 | Convert 212.5 degC to K. Return the converted value with unit. | Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 212.5 + 273.15. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 212.5
} | {
"formula": "value + 273.15",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-3.7, 28.25], "unit": "dimensionless"} | 50ba4c9545b7edbbed80223942aef34d4727dfa5ce676aa35c0c4b66a767439e | medium | {
"answer": [
-3.7,
28.25
],
"unit": "dimensionless"
} | line_two_point_000374_-1_8.5_-3.7_28.25 | Apache-2.0 | A line passes through points (-1, 31.95) and (8.5, -3.2). Return [slope, intercept] for y = slope*x + intercept. | The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order. | programmatic_synthetic_verified | train | linear_modeling | {
"x1": -1,
"x2": 8.5,
"y1": 31.95,
"y2": -3.2
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.
```python
def safe_mean_000376(values):
if not values:
raise ValueError('safe_mean requires at least one value')
return sum(values) / len(valu... | 4dbada16f2d66c312d817eaf927aeecb989cd02cb80ed521302d9030ab33ec65 | medium | {
"answer": "python_code",
"function": "safe_mean_000376"
} | code_000376_safe_mean_000376 | Apache-2.0 | Write a Python function safe_mean_000376(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block. | Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs. | programmatic_synthetic_verified | train | python_code_generation | {
"function": "safe_mean_000376"
} | {
"function": "safe_mean_000376",
"tests": [
"assert safe_mean_000376([2, 4, 6]) == 4",
"xs = [1, 2, 3]; assert safe_mean_000376(xs) == 2 and xs == [1, 2, 3]",
"try:\n safe_mean_000376([])\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass"
],
"type": "python_tests"
} |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missi... | 87b767410f8246a3a1f8f4a56034d76f4cba9246addc7ed1e1c45f4c89acbd66 | hard | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"recurrence",
"objective",
"tie_breaking_rule"
]
} | abstain_000377_recurrence_objective_tie_breaking_rule | Apache-2.0 | Write a dynamic-programming solver for a routing scoring problem with 4091 items and budget 73190, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: recurrence, objective, tie_breaking_rule.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | code_abstention | {
"missing": [
"recurrence",
"objective",
"tie_breaking_rule"
]
} | {
"missing": [
"recurrence",
"objective",
"tie_breaking_rule"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14 kg and a = 2.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 30.1, "unit": "N"} | ef48afdb25f1f3cedf0498dc35a4ea3b3f7b522555dd229bc27834ff2d5c95d7 | easy | {
"answer": 30.1,
"unit": "N"
} | force_000378_14_2.15 | Apache-2.0 | A cart has mass 14 kg and measured acceleration 2.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 14 kg and a = 2.15 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 2.15,
"mass": 14
} | {
"formula": "mass * acceleration",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.5^2 and multiply by 0.5 * 18.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 17787.15, "unit": "J"} | 48cc74ce4cb81e5667fbdb3be3f8a283733ab0cbc2ac9588fda6ea9e8b2dfb90 | easy | {
"answer": 17787.15,
"unit": "J"
} | ke_000379_18.8_43.5 | Apache-2.0 | A body of mass 18.8 kg moves at 43.5 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.5^2 and multiply by 0.5 * 18.8.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 18.8,
"velocity": 43.5
} | {
"formula": "0.5 * mass * velocity ** 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=71 degrees through the sine of 2 theta.
3. Substitute v=80.5 m/s and g=9.81 m/s^2.
Final: {"answer": 406.6912, "unit": "m"} | 9edf1d1a214d1182a244083deb32cff847d6b305b7c8b3783c46b38b91de066f | medium | {
"answer": 406.6912,
"unit": "m"
} | projectile_range_000380_80.5_71 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 80.5 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=80.5 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 71,
"gravity": 9.81,
"speed": 80.5
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 105 * 3.47 * 79.
Final: {"answer": 28783.65, "unit": "J"} | 61433632ef31577085a7500db7102e6c48972c1032d24e683dfe78b4737602a1 | easy | {
"answer": 28783.65,
"unit": "J"
} | heat_q_000382_105_3.47_79 | Apache-2.0 | A 105 g sample has specific heat 3.47 J/(g*K). How much heat is needed to raise its temperature by 79 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 105 * 3.47 * 79. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 79,
"heat_capacity": 3.47,
"mass_g": 105
} | {
"formula": "mass_g * heat_capacity * delta_t",
"tolerance": 0.0001,
"type": "formula"
} |
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