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. Use Newton's second law F = m a.
2. Substitute m = 1.2 kg and a = 8.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 10.38, "unit": "N"} | 09c20bea4bab126a6948c4bb6f125d7bfaab1b3bd6b6e6806d6108e8535143b6 | easy | {
"answer": 10.38,
"unit": "N"
} | force_000000_1.2_8.65 | Apache-2.0 | A cart has mass 1.2 kg and measured acceleration 8.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 1.2 kg and a = 8.65 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 8.65,
"mass": 1.2
} | {
"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 = 23.35^2 and multiply by 0.5 * 18.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5111.4609, "unit": "J"} | 83706137a30aa1590c56a01413f955d1e5b809c741e69197790e83b1c7c188a8 | easy | {
"answer": 5111.4609,
"unit": "J"
} | ke_000001_18.75_23.35 | Apache-2.0 | A body of mass 18.75 kg moves at 23.35 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.35^2 and multiply by 0.5 * 18.75.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 18.75,
"velocity": 23.35
} | {
"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=45 degrees through the sine of 2 theta.
3. Substitute v=10.8 m/s and g=9.81 m/s^2.
Final: {"answer": 11.8899, "unit": "m"} | 04201160189895fd03a25b5efba393fd75a3df315577c20e01a0d6beb6d3673e | medium | {
"answer": 11.8899,
"unit": "m"
} | projectile_range_000002_10.8_45 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 10.8 m/s and angle 45 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=45 degrees through the sine of 2 theta.
Substitute v=10.8 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 45,
"gravity": 9.81,
"speed": 10.8
} | {
"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 = 1210 * 2.365 * 10.
Final: {"answer": 28616.5, "unit": "J"} | 5a7f93e3c157237db74bb7b1dc7e5d7d21d8efd318b98339ea65e981290ec0b4 | easy | {
"answer": 28616.5,
"unit": "J"
} | heat_q_000004_1210_2.365_10 | Apache-2.0 | A 1210 g sample has specific heat 2.365 J/(g*K). How much heat is needed to raise its temperature by 10 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1210 * 2.365 * 10. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 10,
"heat_capacity": 2.365,
"mass_g": 1210
} | {
"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=35 V and R=195.1 ohm.
Final: {"answer": 6.2788, "unit": "W"} | 8064f52e5c6334c49458c8a4fdb66697a0f6bcd33959332678f12297a741648b | easy | {
"answer": 6.2788,
"unit": "W"
} | ohm_power_000005_35_195.1 | Apache-2.0 | A resistor has resistance 195.1 ohm and voltage 35 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=35 V and R=195.1 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 195.1,
"voltage": 35
} | {
"formula": "voltage ** 2 / resistance",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.36 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 236.2053, "unit": "g"} | 6ea9c865703a8b85cfa75b2907ca5e4161fbdb8ec2df6fef81443b35262ee2f8 | medium | {
"answer": 236.2053,
"unit": "g"
} | stoich_mass_000007_calcium_carbonate_2.36 | Apache-2.0 | A sample contains 2.36 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 2.36 mol * 100.087 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "calcium carbonate",
"molar_mass": 100.087,
"moles": 2.36
} | {
"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) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 15.6617, "unit": "state_units"} | 0373e8d6fdf1dfc6322fd1fecc0d7fb58da64971babdc1e3489fcdde8fd1a983 | medium | {
"answer": 15.6617,
"unit": "state_units"
} | euler_decay_000009_69_0.78_0.5_3 | Apache-2.0 | Use explicit Euler on dy/dt = -0.78 y with y(0)=69, step size h=0.5, for 3 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 3 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 69,
"rate": 0.78,
"step": 0.5,
"steps": 3
} | {
"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=0.28 and add it to the current value.
Final: {"answer": [1.566, 1.956, 2.13], "unit": "temperature_units"} | 529b08cc3dcbea632c37d5fbea4e92c251256ec70cd191394c6910dda4ee50cb | hard | {
"answer": [
1.566,
1.956,
2.13
],
"unit": "temperature_units"
} | heat_step_000011_0.28_1.45_1.65_1.55_2.9_1.5 | 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=1.45, right=1.5; current interior values are [1.65, 1.55, 2.9]. 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": [
1.65,
1.55,
2.9
],
"left": 1.45,
"r": 0.28,
"right": 1.5
} | {
"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 -20.5 + 273.15.
Final: {"answer": 252.65, "unit": "K"} | 081e4f571b3127f8ad607a78e7a385e62956f2c6ff5029e25f6a021d39582e1b | easy | {
"answer": 252.65,
"unit": "K"
} | unit_convert_000012_c_to_k_-20.5 | Apache-2.0 | Convert -20.5 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 -20.5 + 273.15. | programmatic_synthetic_verified | train | unit_conversion | {
"value": -20.5
} | {
"formula": "value + 273.15",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"} | 00993ceed0409c2a599fd8dfbb972d370dbb9747d8b5137b7fea981a40db8aa4 | medium | {
"answer": "consistent"
} | dimensional_000015_consistent_4153435f_131890 | Apache-2.0 | In model card equation case 131890, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason. | Compare the dimensions on both sides of the equation.
grams cancel with J/(g*K), and kelvin cancels, leaving joules
The equation is valid only if both sides have identical dimensions. | programmatic_synthetic_verified | train | dimensional_analysis | {
"answer": "consistent",
"equation": "Q = m * c * DeltaT"
} | {
"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 weighted_sum_000016(values, weights):
if len(values) != len(weights):
raise ValueError('length mismatch')
return sum(value * wei... | 3c520a77aff0c6c0f6d3a4a0326b0bbab6f0c31d35d9d1c4a859fab9965128b5 | medium | {
"answer": "python_code",
"function": "weighted_sum_000016"
} | code_000016_weighted_sum_000016 | Apache-2.0 | Write a Python function weighted_sum_000016(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block. | 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_000016"
} | {
"function": "weighted_sum_000016",
"tests": [
"assert weighted_sum_000016([2, 3], [4, 5]) == 23",
"assert weighted_sum_000016([], []) == 0",
"try:\n weighted_sum_000016([1], [1, 2])\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass"
],
"type": "python_tests"
} |
science_math_code | Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=34 degrees through the sine of 2 theta.
3. Substitute v=60.7 m/s and g=9.81 m/s^2.
Final: {"answer": 348.2365, "unit": "m"} | d8d40fe1c3a47d30dc93b5318b0db91c4d7ff9266893afdaebc4be4df32e62fd | medium | {
"answer": 348.2365,
"unit": "m"
} | projectile_range_000020_60.7_34 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 60.7 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=34 degrees through the sine of 2 theta.
Substitute v=60.7 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 34,
"gravity": 9.81,
"speed": 60.7
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"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=200.3 V and R=93.4 ohm.
Final: {"answer": 429.5513, "unit": "W"} | 129aee5c8ea19cdd67c9b8371e3d561a69caa5b7bee60ec5130f9d0e7ea36043 | easy | {
"answer": 429.5513,
"unit": "W"
} | ohm_power_000023_200.3_93.4 | Apache-2.0 | A resistor has resistance 93.4 ohm and voltage 200.3 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=200.3 V and R=93.4 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 93.4,
"voltage": 200.3
} | {
"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=789.5 mg, t=296.5 h, and T_half=47.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 10.4302, "unit": "mg"} | 3ba2cd84feaf26933e1df14deb7d210e741397aaa3871c9f897d5e5505e6053f | medium | {
"answer": 10.4302,
"unit": "mg"
} | half_life_000024_789.5_47.5_296.5 | Apache-2.0 | A radioactive sample starts with 789.5 mg. Its half-life is 47.5 hours. How many mg remain after 296.5 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=789.5 mg, t=296.5 h, and T_half=47.5 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 296.5,
"half_life": 47.5,
"initial_amount": 789.5
} | {
"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 = 1.47 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 85.9068, "unit": "g"} | e7751515430579a1ac31ec36eb4c3d52d2706e83cbe0fa796cc28f4437e45ba0 | medium | {
"answer": 85.9068,
"unit": "g"
} | stoich_mass_000025_sodium_chloride_1.47 | Apache-2.0 | A sample contains 1.47 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 = 1.47 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": 1.47
} | {
"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 1100 mL to 1.1 L.
3. Compute M = 1.005 / 1.1.
Final: {"answer": 0.9136, "unit": "mol/L"} | 6fb33aad72a7943e617a33172b11769ce5aa9f42a0110e990ad4648770e00db7 | medium | {
"answer": 0.9136000000000001,
"unit": "mol/L"
} | molarity_000026_1.005_1100 | Apache-2.0 | A solution contains 1.005 mol of solute in 1100 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 1100 mL to 1.1 L.
Compute M = 1.005 / 1.1. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 1.005,
"volume_ml": 1100
} | {
"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) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 7.0267, "unit": "state_units"} | 1f84531eacd6fcf9befbe9fa91b915ee78072550b366e7b962b1c3a802528193 | medium | {
"answer": 7.0267,
"unit": "state_units"
} | euler_decay_000027_9_0.08_0.75_4 | Apache-2.0 | Use explicit Euler on dy/dt = -0.08 y with y(0)=9, step size h=0.75, for 4 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
Apply that update for 4 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 9,
"rate": 0.08,
"step": 0.75,
"steps": 4
} | {
"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(-7.3)=-33.84 and f(-6.3)=-30.04.
3. The interval width is 1.
Final: {"answer": -31.94, "unit": "area_units"} | fc7106612533edb6fe4fd304c9c55795c35a60328a79e27251ba387bff18f70e | medium | {
"answer": -31.94,
"unit": "area_units"
} | trapz_linear_000028_3.8_-6.1_-7.3_-6.3 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+-6.1 from x=-7.3 to x=-6.3. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.3)=-33.84 and f(-6.3)=-30.04.
The interval width is 1. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": -6.1,
"slope": 3.8,
"x0": -7.3,
"x1": -6.3
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 176.5 + 273.15.
Final: {"answer": 449.65, "unit": "K"} | 277ce7941d09914595050b9493e30b7b7875b81af811d76f9b1ff0dced92d809 | easy | {
"answer": 449.65,
"unit": "K"
} | unit_convert_000030_c_to_k_176.5 | Apache-2.0 | Convert 176.5 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 176.5 + 273.15. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 176.5
} | {
"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": [-6.1, -1.75], "unit": "dimensionless"} | 1f37ffb46d5b9d28cee258944676c8bf1559150fab09b8b830dd2baebb415b86 | medium | {
"answer": [
-6.1,
-1.75
],
"unit": "dimensionless"
} | line_two_point_000032_-10.5_1.75_-6.1_-1.75 | Apache-2.0 | A line passes through points (-10.5, 62.3) and (1.75, -12.425). 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": -10.5,
"x2": 1.75,
"y1": 62.3,
"y2": -12.425
} | {
"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"} | 99779b846f47c792e3848539c4db17e845e5afdb42c7efb7fe9ce8f9d64e8211 | medium | {
"answer": "inconsistent"
} | dimensional_000033_inconsistent_c1271127_463582 | Apache-2.0 | In simulation spec case 463582, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason. | 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 safe_mean_000034(values):
if not values:
raise ValueError('safe_mean requires at least one value')
return sum(values) / len(valu... | ef369f9dc91b9ac4354fc88811e27c7e3ed1ea081bf9f7a2aa74155b36bbebb0 | medium | {
"answer": "python_code",
"function": "safe_mean_000034"
} | code_000034_safe_mean_000034 | Apache-2.0 | Write a Python function safe_mean_000034(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block. | 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_000034"
} | {
"function": "safe_mean_000034",
"tests": [
"assert safe_mean_000034([2, 4, 6]) == 4",
"xs = [1, 2, 3]; assert safe_mean_000034(xs) == 2 and xs == [1, 2, 3]",
"try:\n safe_mean_000034([])\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass"
],
"type": "python_tests"
} |
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... | dd4c58d32e64fcca1413160d597eeb1f0683e8a0771cb6707858628c925972d2 | hard | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"rate_constant",
"number_of_steps"
]
} | abstain_000035_rate_constant_number_of_steps | Apache-2.0 | Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=44 and h=1.45, but omits both k and the number of steps. If there is insufficient information, say so explicitly. | 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 = 14.4 kg and a = 12.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 186.48, "unit": "N"} | 1544364f2a4aed612561d024e305cf84610983a2b8869aace2fceae1bbdde396 | easy | {
"answer": 186.48,
"unit": "N"
} | force_000036_14.4_12.95 | Apache-2.0 | A cart has mass 14.4 kg and measured acceleration 12.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 14.4 kg and a = 12.95 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 12.95,
"mass": 14.4
} | {
"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 = 6.3^2 and multiply by 0.5 * 4.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 89.3025, "unit": "J"} | 92c6dd34a2598cc41361f49ae6641a7108108a23e8359ac45119c434a1448f6d | easy | {
"answer": 89.3025,
"unit": "J"
} | ke_000037_4.5_6.3 | Apache-2.0 | A body of mass 4.5 kg moves at 6.3 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.3^2 and multiply by 0.5 * 4.5.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 4.5,
"velocity": 6.3
} | {
"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=71 degrees through the sine of 2 theta.
3. Substitute v=7.6 m/s and g=9.81 m/s^2.
Final: {"answer": 3.6249, "unit": "m"} | 280268c9dc5de6869e5d40676561d314f9a30c7029f13ed7ec949668b3b980f5 | medium | {
"answer": 3.6249000000000002,
"unit": "m"
} | projectile_range_000038_7.6_71 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 7.6 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=7.6 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 71,
"gravity": 9.81,
"speed": 7.6
} | {
"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 = 5.46 * 8.314 * 482 / 94.0.
Final: {"answer": 232.7672, "unit": "kPa"} | c9d9f9e4bc661ac291d058e7876cd5471aea3391fc5650c30a9154cebc158f3a | medium | {
"answer": 232.7672,
"unit": "kPa"
} | ideal_gas_000039_5.46_482_94.0 | Apache-2.0 | An ideal gas sample has n=5.46 mol, T=482 K, and V=94.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | 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 = 5.46 * 8.314 * 482 / 94.0. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 5.46,
"temp_k": 482,
"volume_l": 94
} | {
"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 = 55 * 4.66 * 75.
Final: {"answer": 19222.5, "unit": "J"} | 0ae96c4b209e502afbdfb47037a355a4112e665f1eab49621f7897d0b4ebb822 | easy | {
"answer": 19222.5,
"unit": "J"
} | heat_q_000040_55_4.66_75 | Apache-2.0 | A 55 g sample has specific heat 4.66 J/(g*K). How much heat is needed to raise its temperature by 75 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 55 * 4.66 * 75. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 75,
"heat_capacity": 4.66,
"mass_g": 55
} | {
"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=562 mg, t=287 h, and T_half=68.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 30.7954, "unit": "mg"} | 8188a5284f52f5c045a816c198d322748e595f621209cc60c5ecbaec51d232f1 | medium | {
"answer": 30.7954,
"unit": "mg"
} | half_life_000042_562_68.5_287 | Apache-2.0 | A radioactive sample starts with 562 mg. Its half-life is 68.5 hours. How many mg remain after 287 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=562 mg, t=287 h, and T_half=68.5 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 287,
"half_life": 68.5,
"initial_amount": 562
} | {
"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 = 7.31 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 321.7131, "unit": "g"} | d6c8d258205a14c558be125e98c58431e474bf86f0ade61ced100fc2ceac3735 | medium | {
"answer": 321.7131,
"unit": "g"
} | stoich_mass_000043_carbon_dioxide_7.31 | Apache-2.0 | A sample contains 7.31 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 = 7.31 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": 7.31
} | {
"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 3185 mL to 3.185 L.
3. Compute M = 4.765 / 3.185.
Final: {"answer": 1.4961, "unit": "mol/L"} | 70023d191a16ef61a48b7e7223f91337bd1d997b25170631c07f09b7cf729c63 | medium | {
"answer": 1.4961,
"unit": "mol/L"
} | molarity_000044_4.765_3185 | Apache-2.0 | A solution contains 4.765 mol of solute in 3185 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 3185 mL to 3.185 L.
Compute M = 4.765 / 3.185. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 4.765,
"volume_ml": 3185
} | {
"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(-9.1)=19.8 and f(-6.3)=14.2.
3. The interval width is 2.8.
Final: {"answer": 47.6, "unit": "area_units"} | 71d13d67e0b8d9352387a9a6eb8323ec3f836e69977b8f3e8974cf5fef979887 | medium | {
"answer": 47.6,
"unit": "area_units"
} | trapz_linear_000046_-2_1.6_-9.1_-6.3 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=-2x+1.6 from x=-9.1 to x=-6.3. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.1)=19.8 and f(-6.3)=14.2.
The interval width is 2.8. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": 1.6,
"slope": -2,
"x0": -9.1,
"x1": -6.3
} | {
"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=0.3 and add it to the current value.
Final: {"answer": [1.35, 1.81, 1.4], "unit": "temperature_units"} | 724430d322fda90f3849feb39e1cfd99976494885942830bc0b7308832aa80c2 | hard | {
"answer": [
1.35,
1.81,
1.4
],
"unit": "temperature_units"
} | heat_step_000047_0.3_-1.2_2.85_1.9_0.65_1.9 | 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=-1.2, right=1.9; current interior values are [2.85, 1.9, 0.65]. 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": [
2.85,
1.9,
0.65
],
"left": -1.2,
"r": 0.30000000000000004,
"right": 1.9
} | {
"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 19254.0 / 1000.
Final: {"answer": 19.254, "unit": "kg"} | 170105de5c912d8d792bf8d68808938056b1724f778fe56877a6c0a5f6cffb54 | easy | {
"answer": 19.254,
"unit": "kg"
} | unit_convert_000048_g_to_kg_19254 | Apache-2.0 | Convert 19254 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 19254.0 / 1000. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 19254
} | {
"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=90 degrees and keep the unit as newtons.
Final: {"answer": [0.0, 289.5], "unit": "N"} | d5d56e948ac80e593d6444bae4cd5ba52fb533d6e939c3e7e54f0cbbdd37e1ea | medium | {
"answer": [
0,
289.5
],
"unit": "N"
} | vector_components_000049_289.5_90 | Apache-2.0 | A vector has magnitude 289.5 N at 90 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=90 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 90,
"magnitude": 289.5
} | {
"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": [0.0, -20.75], "unit": "dimensionless"} | 256bd3b3a25f745ee2f5022faa0da8bf25e4ffb6435104858ca035ce124a110e | medium | {
"answer": [
0,
-20.75
],
"unit": "dimensionless"
} | line_two_point_000050_3.25_16_0_-20.75 | Apache-2.0 | A line passes through points (3.25, -20.75) and (16, -20.75). 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": 3.25,
"x2": 16,
"y1": -20.75,
"y2": -20.75
} | {
"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. mass times acceleration has newton dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"} | d2381fcc3464df2ffd114e2893ea2563c4fef9214e859131ec9667576d592c0e | medium | {
"answer": "consistent"
} | dimensional_000051_consistent_03f5e041_476206 | Apache-2.0 | In lab notebook case 476206, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason. | Compare the dimensions on both sides of the equation.
mass times acceleration has newton dimensions
The equation is valid only if both sides have identical dimensions. | programmatic_synthetic_verified | train | dimensional_analysis | {
"answer": "consistent",
"equation": "F = m * a"
} | {
"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_000052(numerators, denominators):
if len(numerators) != len(denominators):
raise ValueError('length mismatch')
o... | 40f9a1a45b19d843eb4ee8aa7e814c7fbb4ce06a48133c0df1174e1b12b6b35c | medium | {
"answer": "python_code",
"function": "pairwise_ratios_000052"
} | code_000052_pairwise_ratios_000052 | Apache-2.0 | Write a Python function pairwise_ratios_000052(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block. | 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_000052"
} | {
"function": "pairwise_ratios_000052",
"tests": [
"assert pairwise_ratios_000052([2, 9], [4, 3]) == [0.5, 3.0]",
"try:\n pairwise_ratios_000052([1], [0])\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass",
"try:\n pairwise_ratios_000052([1, 2], [1])\n raise 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: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missi... | c9d7b46750dea45dc14e73df96fec20f3ab7692c3777172b526fae025051c0d6 | medium | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"required_fields",
"allowed_transformations"
]
} | abstain_000053_required_fields_allowed_transformations | Apache-2.0 | Write a sanitizer for valid registry survey records in release 430157, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly. | 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 = 16.5 kg and a = 2.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 48.675, "unit": "N"} | 70f3e90c329c21c45b39fe64fc1ceb65dfbce58b0535bf991d25d15130ea1a51 | easy | {
"answer": 48.675,
"unit": "N"
} | force_000054_16.5_2.95 | Apache-2.0 | A cart has mass 16.5 kg and measured acceleration 2.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 16.5 kg and a = 2.95 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 2.95,
"mass": 16.5
} | {
"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 = 13.8^2 and multiply by 0.5 * 24.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2328.129, "unit": "J"} | a57bef5ece3186fb7825fe19cda03e8a299298d1303c8de17e8270f06f414f40 | easy | {
"answer": 2328.129,
"unit": "J"
} | ke_000055_24.45_13.8 | Apache-2.0 | A body of mass 24.45 kg moves at 13.8 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.8^2 and multiply by 0.5 * 24.45.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 24.45,
"velocity": 13.8
} | {
"formula": "0.5 * mass * velocity ** 2",
"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 = 1570 * 1.775 * 1.
Final: {"answer": 2786.75, "unit": "J"} | 726154edb5109f38e2bd61541006bf9b9bf783c230bb44ea9391ce117b0cefe5 | easy | {
"answer": 2786.75,
"unit": "J"
} | heat_q_000058_1570_1.775_1 | Apache-2.0 | A 1570 g sample has specific heat 1.775 J/(g*K). How much heat is needed to raise its temperature by 1 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1570 * 1.775 * 1. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 1,
"heat_capacity": 1.775,
"mass_g": 1570
} | {
"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=173.3 V and R=22.3 ohm.
Final: {"answer": 1346.7664, "unit": "W"} | c0b2ae3e9834a6e85edbcc7dc93f1b5a6f816413e6948d57564b25ea4019bfbb | easy | {
"answer": 1346.7664,
"unit": "W"
} | ohm_power_000059_173.3_22.3 | Apache-2.0 | A resistor has resistance 22.3 ohm and voltage 173.3 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=173.3 V and R=22.3 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 22.3,
"voltage": 173.3
} | {
"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=393 mg, t=221 h, and T_half=109.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 97.014, "unit": "mg"} | 704123ff0a9a4206e2d2fa993c304acad98703013a48613256dbfc6318ed0ce7 | medium | {
"answer": 97.014,
"unit": "mg"
} | half_life_000060_393_109.5_221 | Apache-2.0 | A radioactive sample starts with 393 mg. Its half-life is 109.5 hours. How many mg remain after 221 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=393 mg, t=221 h, and T_half=109.5 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 221,
"half_life": 109.5,
"initial_amount": 393
} | {
"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 = 4.27 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 769.2661, "unit": "g"} | c141cf1e7798c7a01ddda5cb2e42685167a0249a16384c7a4a68f41f885c583e | medium | {
"answer": 769.2661,
"unit": "g"
} | stoich_mass_000061_glucose_4.27 | Apache-2.0 | A sample contains 4.27 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 = 4.27 mol * 180.156 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "glucose",
"molar_mass": 180.156,
"moles": 4.27
} | {
"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) = -0.86 y, so each step multiplies y by 1 - h*0.86.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 1.4324, "unit": "state_units"} | 7ddd1de854ad8599beba76bced92081e967deb76da06e4ddef17aa527324dbfc | medium | {
"answer": 1.4324,
"unit": "state_units"
} | euler_decay_000063_6_0.86_0.35_4 | Apache-2.0 | Use explicit Euler on dy/dt = -0.86 y with y(0)=6, step size h=0.35, for 4 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.86 y, so each step multiplies y by 1 - h*0.86.
Apply that update for 4 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 6,
"rate": 0.86,
"step": 0.35000000000000003,
"steps": 4
} | {
"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)=-11.13 and f(0.3)=6.93.
3. The interval width is 8.6.
Final: {"answer": -18.06, "unit": "area_units"} | b9bef2923c3bde8ddf6b9b60d75f687cab5b09dfb23cce55f2420048720f1f75 | medium | {
"answer": -18.06,
"unit": "area_units"
} | trapz_linear_000064_2.1_6.3_-8.3_0.3 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=2.1x+6.3 from x=-8.3 to x=0.3. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.3)=-11.13 and f(0.3)=6.93.
The interval width is 8.6. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": 6.3,
"slope": 2.1,
"x0": -8.3,
"x1": 0.30000000000000004
} | {
"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": [0.809, 1.448, 0.869], "unit": "temperature_units"} | 0fdd44cf26a669b947baa35355762a810eeaf1f7b6f384f70642473f808244ae | hard | {
"answer": [
0.809,
1.448,
0.869
],
"unit": "temperature_units"
} | heat_step_000065_0.34_-1.9_2.9_1.55_-0.1_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=-1.9, right=1.1; current interior values are [2.9, 1.55, -0.1]. 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": [
2.9,
1.55,
-0.1
],
"left": -1.9,
"r": 0.34,
"right": 1.1
} | {
"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 4181.5 / 100.
Final: {"answer": 41.815, "unit": "m"} | f8e44263bda0d2d6274cb30dac0c3b3967fe96294a5c11a24fd9e97ff0e07922 | easy | {
"answer": 41.815,
"unit": "m"
} | unit_convert_000066_cm_to_m_4181.5 | Apache-2.0 | Convert 4181.5 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 4181.5 / 100. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 4181.5
} | {
"formula": "value / 100",
"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=233 degrees and keep the unit as newtons.
Final: {"answer": [-133.0011, -176.4984], "unit": "N"} | 0669679251b1bde5a2e77f5590cd5f93ed2c4e99d472537cae6e876956250f9b | medium | {
"answer": [
-133.0011,
-176.4984
],
"unit": "N"
} | vector_components_000067_221_233 | Apache-2.0 | A vector has magnitude 221 N at 233 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=233 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 233,
"magnitude": 221
} | {
"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": [-4.0, -0.75], "unit": "dimensionless"} | b7fab05e3dc3f7b1155f8446470aa3704821b9374f43f55bfc26e763e660ab0a | medium | {
"answer": [
-4,
-0.75
],
"unit": "dimensionless"
} | line_two_point_000068_18.25_24.75_-4_-0.75 | Apache-2.0 | A line passes through points (18.25, -73.75) and (24.75, -99.75). 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": 18.25,
"x2": 24.75,
"y1": -73.75,
"y2": -99.75
} | {
"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"} | 326f42a9ba8f001742dd32011e17d053777b1d7a73d7c2252a469de7cf5e9104 | medium | {
"answer": "consistent"
} | dimensional_000069_consistent_8b38953d_89868 | Apache-2.0 | In quality-control check case 89868, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason. | 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_000070(values):
total = sum(values)
if total == 0:
raise ValueError('cannot normalize zero-sum values')
return [v ... | 0b18f591732d0f125e8745c6b8cd1a3bc3479e7c22bae92fa0238a0f7a36d04c | medium | {
"answer": "python_code",
"function": "normalize_000070"
} | code_000070_normalize_000070 | Apache-2.0 | Write a Python function normalize_000070(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block. | 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_000070"
} | {
"function": "normalize_000070",
"tests": [
"out = normalize_000070([2, 3, 5]); assert len(out) == 3",
"assert abs(sum(normalize_000070([2, 3, 5])) - 1.0) < 1e-12",
"assert normalize_000070([1, 1]) == [0.5, 0.5]",
"try:\n normalize_000070([1, -1])\n raise AssertionError('expected ValueError')... |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left... | 8935b841d51b9ca5b1bfdc37472d52050ee7b8ee038e515c207009ec6f4bf49d | medium | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"left_boundary",
"right_boundary"
]
} | abstain_000071_left_boundary_right_boundary | Apache-2.0 | Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [-1.45, -0.9, -1.3], but gives no boundary values. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: left_boundary, right_boundary.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | scientific_abstention | {
"missing": [
"left_boundary",
"right_boundary"
]
} | {
"missing": [
"left_boundary",
"right_boundary"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.6 kg and a = 12.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 249.26, "unit": "N"} | 5ee2b128bce58976a226084be9566cdb438ab1a7a759dca6640bf236ed593432 | easy | {
"answer": 249.26,
"unit": "N"
} | force_000072_20.6_12.1 | Apache-2.0 | A cart has mass 20.6 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 20.6 kg and a = 12.1 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 12.1,
"mass": 20.6
} | {
"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 = 25.6^2 and multiply by 0.5 * 19.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6225.92, "unit": "J"} | 60a843b140436eb7f1a17af5f5e1e0ae84558fb2c35d56e88c7de95e8edad1cf | easy | {
"answer": 6225.92,
"unit": "J"
} | ke_000073_19_25.6 | Apache-2.0 | A body of mass 19 kg moves at 25.6 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.6^2 and multiply by 0.5 * 19.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 19,
"velocity": 25.6
} | {
"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=11.3 m/s and g=9.81 m/s^2.
Final: {"answer": 11.4927, "unit": "m"} | 4a917d2a4f1895eec6ecb470a03703bfebe18c2f5f4f1b19b855727e91608fd9 | medium | {
"answer": 11.4927,
"unit": "m"
} | projectile_range_000074_11.3_59 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 11.3 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=59 degrees through the sine of 2 theta.
Substitute v=11.3 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 59,
"gravity": 9.81,
"speed": 11.3
} | {
"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity",
"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=987 mg, t=86.5 h, and T_half=80.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 468.6516, "unit": "mg"} | a19b8926dd65515b4308251342b06416e09e947d7122a91d5ef56bab5b7aa81e | medium | {
"answer": 468.6516,
"unit": "mg"
} | half_life_000078_987_80.5_86.5 | Apache-2.0 | A radioactive sample starts with 987 mg. Its half-life is 80.5 hours. How many mg remain after 86.5 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=987 mg, t=86.5 h, and T_half=80.5 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 86.5,
"half_life": 80.5,
"initial_amount": 987
} | {
"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 = 6.29 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 629.5472, "unit": "g"} | f2c3844781bd647c73458ea8e348d02db0c86137bfaef61e234aa23440586051 | medium | {
"answer": 629.5472,
"unit": "g"
} | stoich_mass_000079_calcium_carbonate_6.29 | Apache-2.0 | A sample contains 6.29 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 6.29 mol * 100.087 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "calcium carbonate",
"molar_mass": 100.087,
"moles": 6.29
} | {
"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 1180 mL to 1.18 L.
3. Compute M = 2.735 / 1.18.
Final: {"answer": 2.3178, "unit": "mol/L"} | fff4e1d53447784ec2170b74491d5bc7f778e38313436a0488beb84a8d703a72 | medium | {
"answer": 2.3178,
"unit": "mol/L"
} | molarity_000080_2.735_1180 | Apache-2.0 | A solution contains 2.735 mol of solute in 1180 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 1180 mL to 1.18 L.
Compute M = 2.735 / 1.18. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 2.735,
"volume_ml": 1180
} | {
"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) = -0.17 y, so each step multiplies y by 1 - h*0.17.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 17.6153, "unit": "state_units"} | 3792e143db6fa4a0157fa84b7f06a85ee45feefa6bff48a887fbb0eadc1a927d | medium | {
"answer": 17.6153,
"unit": "state_units"
} | euler_decay_000081_66.5_0.17_0.9_8 | Apache-2.0 | Use explicit Euler on dy/dt = -0.17 y with y(0)=66.5, step size h=0.9, for 8 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
Apply that update for 8 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 66.5,
"rate": 0.17,
"step": 0.9,
"steps": 8
} | {
"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(-9.9)=33.73 and f(-2.5)=13.75.
3. The interval width is 7.4.
Final: {"answer": 175.676, "unit": "area_units"} | 5a63f5ddeb5de57e75f28ed780e5450a87fe2a789a3fee117b0bfdb8eed6c46e | medium | {
"answer": 175.676,
"unit": "area_units"
} | trapz_linear_000082_-2.7_7_-9.9_-2.5 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+7 from x=-9.9 to x=-2.5. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.9)=33.73 and f(-2.5)=13.75.
The interval width is 7.4. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": 7,
"slope": -2.7,
"x0": -9.9,
"x1": -2.5
} | {
"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 44644.0 / 1000.
Final: {"answer": 44.644, "unit": "kg"} | 4b1e61afcbd787a29e76e5c521da25b9cdfb587debd09b170c52d8316ded5963 | easy | {
"answer": 44.644,
"unit": "kg"
} | unit_convert_000084_g_to_kg_44644 | Apache-2.0 | Convert 44644 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 44644.0 / 1000. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 44644
} | {
"formula": "value / 1000",
"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": [-8.7, 20.25], "unit": "dimensionless"} | 0162806822173dfe74b7136ad8e212471b361d423510c38d6a49b6aa84bf656a | medium | {
"answer": [
-8.7,
20.25
],
"unit": "dimensionless"
} | line_two_point_000086_1.75_7.5_-8.7_20.25 | Apache-2.0 | A line passes through points (1.75, 5.025) and (7.5, -45). 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": 1.75,
"x2": 7.5,
"y1": 5.025,
"y2": -45
} | {
"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]",
"tolerance": 0.0001,
"type": "formula"
} |
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"]} | 7f8597d3bef67546acffe2d0e407856cadacf660bf5f77928f7a74aacfa8453a | medium | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"volume"
]
} | abstain_000089_volume | Apache-2.0 | Compute pressure from the ideal gas law. The prompt gives n=1.71 mol and T=579 K, but does not give volume. If there is insufficient information, say so explicitly. | 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. Use Newton's second law F = m a.
2. Substitute m = 5.8 kg and a = 13.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 77.72, "unit": "N"} | 1f151c17e5b30f7b46b5024efa1f691d815a21dd2d9324e2dc3f8292f2b59b6b | easy | {
"answer": 77.72,
"unit": "N"
} | force_000090_5.8_13.4 | Apache-2.0 | A cart has mass 5.8 kg and measured acceleration 13.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 5.8 kg and a = 13.4 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 13.4,
"mass": 5.8
} | {
"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 = 9.25^2 and multiply by 0.5 * 20.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 891.9891, "unit": "J"} | 828815539985e09e9785b9b6024ada4045833e16e589c25f418f91dc2aaea728 | easy | {
"answer": 891.9891,
"unit": "J"
} | ke_000091_20.85_9.25 | Apache-2.0 | A body of mass 20.85 kg moves at 9.25 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.25^2 and multiply by 0.5 * 20.85.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 20.85,
"velocity": 9.25
} | {
"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=75 degrees through the sine of 2 theta.
3. Substitute v=74.5 m/s and g=9.81 m/s^2.
Final: {"answer": 282.8874, "unit": "m"} | 6370c18accdcb306d0d05262b5c172721a8408b6f1f2971eb638c42e90cbeb4a | medium | {
"answer": 282.8874,
"unit": "m"
} | projectile_range_000092_74.5_75 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 74.5 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=75 degrees through the sine of 2 theta.
Substitute v=74.5 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 75,
"gravity": 9.81,
"speed": 74.5
} | {
"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 = 5.42 * 8.314 * 570 / 72.9.
Final: {"answer": 352.3357, "unit": "kPa"} | c882e0ac568b345b8a2f5f40d8a0c2eb4c7241199cdfb8227ec95ce555f10bab | medium | {
"answer": 352.3357,
"unit": "kPa"
} | ideal_gas_000093_5.42_570_72.9 | Apache-2.0 | An ideal gas sample has n=5.42 mol, T=570 K, and V=72.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | 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 = 5.42 * 8.314 * 570 / 72.9. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 5.42,
"temp_k": 570,
"volume_l": 72.9
} | {
"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=91.1 V and R=111.4 ohm.
Final: {"answer": 74.4992, "unit": "W"} | 714654d9c62ba8302a75b85510f0afb3aaa1408cce5d4baca4db28e79d0b9b3b | easy | {
"answer": 74.4992,
"unit": "W"
} | ohm_power_000095_91.1_111.4 | Apache-2.0 | A resistor has resistance 111.4 ohm and voltage 91.1 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=91.1 V and R=111.4 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 111.4,
"voltage": 91.1
} | {
"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=754.5 mg, t=143 h, and T_half=84.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 233.4661, "unit": "mg"} | 83a5f64c8c64dc32d12d6aabc0b7c45bd7136f9bff78a706e5ec16a9a5c05f67 | medium | {
"answer": 233.4661,
"unit": "mg"
} | half_life_000096_754.5_84.5_143 | Apache-2.0 | A radioactive sample starts with 754.5 mg. Its half-life is 84.5 hours. How many mg remain after 143 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=754.5 mg, t=143 h, and T_half=84.5 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 143,
"half_life": 84.5,
"initial_amount": 754.5
} | {
"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 355 mL to 0.355 L.
3. Compute M = 4.355 / 0.355.
Final: {"answer": 12.2676, "unit": "mol/L"} | 55b015009458c84a98e644c4d8392b0f24d7c6c12bdd9135661b399170860f81 | medium | {
"answer": 12.2676,
"unit": "mol/L"
} | molarity_000098_4.355_355 | Apache-2.0 | A solution contains 4.355 mol of solute in 355 mL of solution. Compute the molarity in mol/L. | Molarity is moles of solute divided by solution volume in liters.
Convert 355 mL to 0.355 L.
Compute M = 4.355 / 0.355. | programmatic_synthetic_verified | train | chemistry_solutions | {
"moles": 4.355,
"volume_ml": 355
} | {
"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) = -0.87 y, so each step multiplies y by 1 - h*0.87.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 3.8554, "unit": "state_units"} | 5d26fa70e9e9d0b4145467044c135fae5af959e12e249b2ececf7c4cb3fc435b | medium | {
"answer": 3.8554,
"unit": "state_units"
} | euler_decay_000099_47_0.87_0.65_3 | Apache-2.0 | Use explicit Euler on dy/dt = -0.87 y with y(0)=47, step size h=0.65, for 3 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.
Apply that update for 3 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 47,
"rate": 0.87,
"step": 0.65,
"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(0.9)=-13.84 and f(6.1)=-6.56.
3. The interval width is 5.2.
Final: {"answer": -53.04, "unit": "area_units"} | 24c2f6ac28dd852520f92bc75bd1ebee43cfd56e81c407c43f0e8bbe3228df1a | medium | {
"answer": -53.04,
"unit": "area_units"
} | trapz_linear_000100_1.4_-15.1_0.9_6.1 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=1.4x+-15.1 from x=0.9 to x=6.1. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.9)=-13.84 and f(6.1)=-6.56.
The interval width is 5.2. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": -15.1,
"slope": 1.4,
"x0": 0.9,
"x1": 6.1
} | {
"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=0.36 and add it to the current value.
Final: {"answer": [0.802, -0.128, -0.86], "unit": "temperature_units"} | 252c6091088ab7e37ebe695d5844284193115cf7312dac08090611254c5ab77d | hard | {
"answer": [
0.802,
-0.128,
-0.86
],
"unit": "temperature_units"
} | heat_step_000101_0.36_1.85_1.9_-1.1_-1.4_-0.2 | 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=1.85, right=-0.2; current interior values are [1.9, -1.1, -1.4]. 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": [
1.9,
-1.1,
-1.4
],
"left": 1.85,
"r": 0.36,
"right": -0.2
} | {
"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 114.5 + 273.15.
Final: {"answer": 387.65, "unit": "K"} | 9be5b14dfbe353d39d246a820ed4b9f5f1aaeaa7323a45df3cead1c9f7cea522 | easy | {
"answer": 387.65,
"unit": "K"
} | unit_convert_000102_c_to_k_114.5 | Apache-2.0 | Convert 114.5 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 114.5 + 273.15. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 114.5
} | {
"formula": "value + 273.15",
"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=78 degrees and keep the unit as newtons.
Final: {"answer": [42.6219, 200.5203], "unit": "N"} | e246de3bb772749e3cfcb628270b47d5b77872796704d12f55ffa4d05f9caa88 | medium | {
"answer": [
42.6219,
200.5203
],
"unit": "N"
} | vector_components_000103_205_78 | Apache-2.0 | A vector has magnitude 205 N at 78 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=78 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 78,
"magnitude": 205
} | {
"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": [-8.85, -16.0], "unit": "dimensionless"} | bbe4502e7d6c9a801c2ffec55aa442bc8515714c3ddfe01d3cc8654a5131ca04 | medium | {
"answer": [
-8.85,
-16
],
"unit": "dimensionless"
} | line_two_point_000104_-13.5_-6.75_-8.85_-16 | Apache-2.0 | A line passes through points (-13.5, 103.475) and (-6.75, 43.7375). 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": -13.5,
"x2": -6.75,
"y1": 103.475,
"y2": 43.7375
} | {
"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. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"} | 655b2ebecaa4a028bc064d0b2da86e7a630df898ec113f9c48f2f741a5da7d09 | medium | {
"answer": "consistent"
} | dimensional_000105_consistent_741d4e34_426072 | Apache-2.0 | In student derivation case 426072, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason. | Compare the dimensions on both sides of the equation.
speed squared over acceleration has units of meters
The equation is valid only if both sides have identical dimensions. | programmatic_synthetic_verified | train | dimensional_analysis | {
"answer": "consistent",
"equation": "R = v^2 * sin(theta) / g"
} | {
"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 clamp_000106(x, lo, hi):
if lo > hi:
raise ValueError('lo must be <= hi')
return min(max(x, lo), hi)
```
Final: {"answer": "pyth... | d5d30a2ee2b483e584831a97d472d16ee5ee45d682c7ccb5a42da537a834f1d9 | medium | {
"answer": "python_code",
"function": "clamp_000106"
} | code_000106_clamp_000106 | Apache-2.0 | Write a Python function clamp_000106(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block. | 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": "clamp_000106"
} | {
"function": "clamp_000106",
"tests": [
"assert clamp_000106(5, 0, 10) == 5",
"assert clamp_000106(-2, 0, 10) == 0",
"assert clamp_000106(12, 0, 10) == 10",
"try:\n clamp_000106(1, 3, 2)\n raise AssertionError('expected ValueError')\nexcept ValueError:\n pass"
],
"type": "python_tests"... |
science_math_code | Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["targ... | b8ae608a74582856820195192976708339955b64c354341a26f84c9c494eed0b | medium | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"target_schema",
"valid_examples"
]
} | abstain_000107_target_schema_valid_examples | Apache-2.0 | Write a parser that converts each warehouse crop record from batch 305743 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly. | Check whether all variables required by the governing equation or specification are present.
The missing required information is: target_schema, valid_examples.
A numeric or code answer would require inventing unstated assumptions, so abstain. | programmatic_synthetic_verified | train | code_abstention | {
"missing": [
"target_schema",
"valid_examples"
]
} | {
"missing": [
"target_schema",
"valid_examples"
],
"type": "abstention"
} |
science_math_code | Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.45 kg and a = 5.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 74.4175, "unit": "N"} | 1040212e97e0686568aa32ce6c032e2cd33863aebe81e810c8b71f88a645dcfd | easy | {
"answer": 74.4175,
"unit": "N"
} | force_000108_14.45_5.15 | Apache-2.0 | A cart has mass 14.45 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 14.45 kg and a = 5.15 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 5.15,
"mass": 14.45
} | {
"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 = 6.7^2 and multiply by 0.5 * 15.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 346.7752, "unit": "J"} | f70ca2b7906cf3901c763688ccdea5ebf1b2b6442ceb4142bd4efad10e1bb0a3 | easy | {
"answer": 346.7752,
"unit": "J"
} | ke_000109_15.45_6.7 | Apache-2.0 | A body of mass 15.45 kg moves at 6.7 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.7^2 and multiply by 0.5 * 15.45.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 15.45,
"velocity": 6.7
} | {
"formula": "0.5 * mass * velocity ** 2",
"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 = 4.42 * 8.314 * 388 / 25.5.
Final: {"answer": 559.1442, "unit": "kPa"} | 017866bef0afd586f14f704e7924d291dbfe0b7b5a15c756a663074922dbb3ae | medium | {
"answer": 559.1442,
"unit": "kPa"
} | ideal_gas_000111_4.42_388_25.5 | Apache-2.0 | An ideal gas sample has n=4.42 mol, T=388 K, and V=25.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | 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 = 4.42 * 8.314 * 388 / 25.5. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 4.42,
"temp_k": 388,
"volume_l": 25.5
} | {
"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=29.7 V and R=165.7 ohm.
Final: {"answer": 5.3234, "unit": "W"} | 2dbe4ae6179c91f6f75017c081cc76cef42d34d4218169aef2163f31883d365b | easy | {
"answer": 5.3234,
"unit": "W"
} | ohm_power_000113_29.7_165.7 | Apache-2.0 | A resistor has resistance 165.7 ohm and voltage 29.7 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=29.7 V and R=165.7 ohm. | programmatic_synthetic_verified | train | electric_circuits | {
"resistance": 165.7,
"voltage": 29.7
} | {
"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=613.5 mg, t=233 h, and T_half=80.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 82.5107, "unit": "mg"} | a7a904bc47f80c8341a11fda30e9d01614ab4435f122b2d143009b3bb5d14807 | medium | {
"answer": 82.5107,
"unit": "mg"
} | half_life_000114_613.5_80.5_233 | Apache-2.0 | A radioactive sample starts with 613.5 mg. Its half-life is 80.5 hours. How many mg remain after 233 hours? | Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=613.5 mg, t=233 h, and T_half=80.5 h.
The remaining amount has the same mass unit as the initial amount. | programmatic_synthetic_verified | train | exponential_decay | {
"elapsed_time": 233,
"half_life": 80.5,
"initial_amount": 613.5
} | {
"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 = 2.56 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 149.6064, "unit": "g"} | 3603ca23738155d7a92ab257b820b9a7c393494158cdd39b22789971498053ea | medium | {
"answer": 149.6064,
"unit": "g"
} | stoich_mass_000115_sodium_chloride_2.56 | Apache-2.0 | A sample contains 2.56 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 = 2.56 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": 2.56
} | {
"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) = -0.88 y, so each step multiplies y by 1 - h*0.88.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"} | e928d0c32aed6aa214237192d53106d147e76aed8fc69e3a5717ba81bcad76bc | medium | {
"answer": 0,
"unit": "state_units"
} | euler_decay_000117_11.5_0.88_1.4_12 | Apache-2.0 | Use explicit Euler on dy/dt = -0.88 y with y(0)=11.5, step size h=1.4, for 12 steps. What is y after the final step? | Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
Apply that update for 12 steps and round the final state. | programmatic_synthetic_verified | train | numerical_ode | {
"initial_y": 11.5,
"rate": 0.88,
"step": 1.4,
"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(3.3)=21.48 and f(12.8)=55.68.
3. The interval width is 9.5.
Final: {"answer": 366.51, "unit": "area_units"} | 9db8a75821cd73f00b73dbb5fac9e330ae3f3f04922037b51b46553c161ef56e | medium | {
"answer": 366.51,
"unit": "area_units"
} | trapz_linear_000118_3.6_9.6_3.3_12.8 | Apache-2.0 | Use the trapezoid rule with one interval to approximate the integral of f(x)=3.6x+9.6 from x=3.3 to x=12.8. Return the numeric integral estimate. | The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.3)=21.48 and f(12.8)=55.68.
The interval width is 9.5. | programmatic_synthetic_verified | train | numerical_integration | {
"intercept": 9.6,
"slope": 3.6,
"x0": 3.3,
"x1": 12.8
} | {
"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=0.4 and add it to the current value.
Final: {"answer": [0.18, -0.7, -0.37], "unit": "temperature_units"} | 099e13a3ba3a89ef291a63b31981c6a7961f6012c74cf67ab243c4308846604b | hard | {
"answer": [
0.18,
-0.7000000000000001,
-0.37
],
"unit": "temperature_units"
} | heat_step_000119_0.4_-0.15_-1.6_1.4_-0.85_-1.9 | 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=-0.15, right=-1.9; current interior values are [-1.6, 1.4, -0.85]. Use r=0.4. 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=0.4 and add it to the current value. | programmatic_synthetic_verified | train | finite_difference_pde | {
"interior": [
-1.6,
1.4,
-0.85
],
"left": -0.15,
"r": 0.4,
"right": -1.9
} | {
"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 4606.5 / 100.
Final: {"answer": 46.065, "unit": "m"} | ecc482a0dd3f47133fd5320f3092b07f3ffb1a67497ed7a2f7ec2cafa4928c46 | easy | {
"answer": 46.065,
"unit": "m"
} | unit_convert_000120_cm_to_m_4606.5 | Apache-2.0 | Convert 4606.5 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 4606.5 / 100. | programmatic_synthetic_verified | train | unit_conversion | {
"value": 4606.5
} | {
"formula": "value / 100",
"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=201 degrees and keep the unit as newtons.
Final: {"answer": [-397.7053, -152.6647], "unit": "N"} | 07bfada1befddd03d67df0a4d5d4eace281fa7f3b8776aa6d760c2051ab63ed5 | medium | {
"answer": [
-397.7053,
-152.6647
],
"unit": "N"
} | vector_components_000121_426_201 | Apache-2.0 | A vector has magnitude 426 N at 201 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=201 degrees and keep the unit as newtons. | programmatic_synthetic_verified | train | vector_reasoning | {
"angle_deg": 201,
"magnitude": 426
} | {
"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. 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"} | d89d9f08fc265701d424a312903f907d285d0765ac870ca1002893251b19f610 | medium | {
"answer": "inconsistent"
} | dimensional_000123_inconsistent_1e14b074_384919 | Apache-2.0 | In instrument manual case 384919, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason. | 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: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]} | 164bad3e381acc6ed9ce173086881cb9a30f5e16c69e4323f2e6dce0700bf56e | medium | {
"answer": "INSUFFICIENT_INFO",
"missing": [
"volume"
]
} | abstain_000125_volume | Apache-2.0 | Compute pressure from the ideal gas law. The prompt gives n=5.89 mol and T=458 K, but does not give volume. If there is insufficient information, say so explicitly. | 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. Use Newton's second law F = m a.
2. Substitute m = 23.65 kg and a = 12.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 297.99, "unit": "N"} | 889d9168e7fd8289ad0b5acca7e3c76b66144ba15b57393f95b9652419c5064a | easy | {
"answer": 297.99,
"unit": "N"
} | force_000126_23.65_12.6 | Apache-2.0 | A cart has mass 23.65 kg and measured acceleration 12.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning. | Use Newton's second law F = m a.
Substitute m = 23.65 kg and a = 12.6 m/s^2.
The unit kg*m/s^2 is one newton. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"acceleration": 12.6,
"mass": 23.65
} | {
"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 = 3.15^2 and multiply by 0.5 * 8.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 43.9071, "unit": "J"} | db6416f992c2b1c78b576ebc8a9f19442e45960f08dc17aca3a0682d6fb5a34a | easy | {
"answer": 43.9071,
"unit": "J"
} | ke_000127_8.85_3.15 | Apache-2.0 | A body of mass 8.85 kg moves at 3.15 m/s. Find its kinetic energy in joules with unit reasoning. | Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.15^2 and multiply by 0.5 * 8.85.
The unit kg*m^2/s^2 is one joule. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"mass": 8.85,
"velocity": 3.15
} | {
"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=29 degrees through the sine of 2 theta.
3. Substitute v=78.1 m/s and g=9.81 m/s^2.
Final: {"answer": 527.2949, "unit": "m"} | abc8cea16da173fe7217e07637bfb363d4907772acef52b8316d30d4dc56605a | medium | {
"answer": 527.2949,
"unit": "m"
} | projectile_range_000128_78.1_29 | Apache-2.0 | A projectile is launched on level ground with no air resistance at speed 78.1 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2. | For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=29 degrees through the sine of 2 theta.
Substitute v=78.1 m/s and g=9.81 m/s^2. | programmatic_synthetic_verified | train | unit_checked_mechanics | {
"angle_deg": 29,
"gravity": 9.81,
"speed": 78.1
} | {
"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 = 1.8 * 8.314 * 371 / 28.6.
Final: {"answer": 194.129, "unit": "kPa"} | 52cc9508a4d60184a9150989b29b6570186f04f5daa36b290573b3bbada1afec | medium | {
"answer": 194.129,
"unit": "kPa"
} | ideal_gas_000129_1.8_371_28.6 | Apache-2.0 | An ideal gas sample has n=1.8 mol, T=371 K, and V=28.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa. | 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 = 1.8 * 8.314 * 371 / 28.6. | programmatic_synthetic_verified | train | thermodynamics | {
"n_mol": 1.8,
"temp_k": 371,
"volume_l": 28.6
} | {
"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 = 525 * 3.36 * 108.
Final: {"answer": 190512.0, "unit": "J"} | bf451c979c85fee90d29082719ac44f0c185503b12b6e44e22c0c655dcea04db | easy | {
"answer": 190512,
"unit": "J"
} | heat_q_000130_525_3.36_108 | Apache-2.0 | A 525 g sample has specific heat 3.36 J/(g*K). How much heat is needed to raise its temperature by 108 K? | Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 525 * 3.36 * 108. | programmatic_synthetic_verified | train | thermodynamics | {
"delta_t": 108,
"heat_capacity": 3.36,
"mass_g": 525
} | {
"formula": "mass_g * heat_capacity * delta_t",
"tolerance": 0.0001,
"type": "formula"
} |
science_math_code | Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.81 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 81.0705, "unit": "g"} | 1564d0e22cfc4f600b322f37adfd10ccae0f760a4083a5f4f3a88bc3ffba1667 | medium | {
"answer": 81.0705,
"unit": "g"
} | stoich_mass_000133_calcium_carbonate_0.81 | Apache-2.0 | A sample contains 0.81 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams. | Mass equals amount in moles times molar mass.
Use m = 0.81 mol * 100.087 g/mol.
The mole unit cancels, leaving grams. | programmatic_synthetic_verified | train | chemistry_stoichiometry | {
"compound": "calcium carbonate",
"molar_mass": 100.087,
"moles": 0.81
} | {
"formula": "moles * molar_mass",
"tolerance": 0.0001,
"type": "formula"
} |
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