Response:
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": [0.695, 0.73, 0.395], "unit": "temperature_units"}

Answer: 0.695

Answer: 0.73

Answer: 0.395

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.5, right=-1.1; current interior values are [0.65, -0.05, 1.85]. Use r=0.3. Return the next interior vector.

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.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 29889.0 / 1000.
Final: {"answer": 29.889, "unit": "kg"}

Answer: 29.889

Prompt: Convert 29889 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 29889.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=153 degrees and keep the unit as newtons.
Final: {"answer": [-40.9863, 20.8836], "unit": "N"}

Answer: -40.9863

Answer: 20.8836

Prompt: A vector has magnitude 46 N at 153 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=153 degrees and keep the unit as newtons.

[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]


Response:
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": [-3.55, -7.0], "unit": "dimensionless"}

Answer: -3.55

Answer: -7.0

Prompt: A line passes through points (-15, 46.25) and (-12.75, 38.2625). 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.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. density times acceleration times height gives kg/(m*s^2), or pascal
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 684771, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
density times acceleration times height gives kg/(m*s^2), or pascal
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
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_000682(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_000682"}

Answer: python_code

Prompt: Write a Python function safe_mean_000682(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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.

try:
    safe_mean_000682([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
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"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.35 mol and T=505 K, but does not give volume. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.95^2 and multiply by 0.5 * 13.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4993.3297, "unit": "J"}

Answer: 4993.3297

Prompt: A body of mass 13.75 kg moves at 26.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.95^2 and multiply by 0.5 * 13.75.
The unit kg*m^2/s^2 is one joule.


Response:
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 = 2.17 * 8.314 * 584 / 68.5.
Final: {"answer": 153.8126, "unit": "kPa"}

Answer: 153.8126

Prompt: An ideal gas sample has n=2.17 mol, T=584 K, and V=68.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 2.17 * 8.314 * 584 / 68.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 740 * 2.175 * 48.
Final: {"answer": 77256.0, "unit": "J"}

Answer: 77256.0

Prompt: A 740 g sample has specific heat 2.175 J/(g*K). How much heat is needed to raise its temperature by 48 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 740 * 2.175 * 48.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=56.3 V and R=196.5 ohm.
Final: {"answer": 16.1307, "unit": "W"}

Answer: 16.1307

Prompt: A resistor has resistance 196.5 ohm and voltage 56.3 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=56.3 V and R=196.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=65 mg, t=97 h, and T_half=21 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 2.6451, "unit": "mg"}

Answer: 2.6451

Prompt: A radioactive sample starts with 65 mg. Its half-life is 21 hours. How many mg remain after 97 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=65 mg, t=97 h, and T_half=21 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.08 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 208.181, "unit": "g"}

Answer: 208.181

Prompt: A sample contains 2.08 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 = 2.08 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3230 mL to 3.23 L.
3. Compute M = 4.465 / 3.23.
Final: {"answer": 1.3824, "unit": "mol/L"}

Answer: 1.3824

Prompt: A solution contains 4.465 mol of solute in 3230 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3230 mL to 3.23 L.
Compute M = 4.465 / 3.23.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 4.7629, "unit": "state_units"}

Answer: 4.7629

Prompt: Use explicit Euler on dy/dt = -0.32 y with y(0)=20, step size h=1.6, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
Apply that update for 2 steps and round the final state.


Response:
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=0.16 and add it to the current value.
Final: {"answer": [1.186, -1.348, -1.664], "unit": "temperature_units"}

Answer: 1.186

Answer: -1.348

Answer: -1.664

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.3, right=0; current interior values are [1.65, -1.9, -2.0]. Use r=0.16. Return the next interior vector.

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=0.16 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 11209.0 / 1000.
Final: {"answer": 11.209, "unit": "kg"}

Answer: 11.209

Prompt: Convert 11209 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 11209.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=307 degrees and keep the unit as newtons.
Final: {"answer": [157.0737, -208.4439], "unit": "N"}

Answer: 157.0737

Answer: -208.4439

Prompt: A vector has magnitude 261 N at 307 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=307 degrees and keep the unit as newtons.


Response:
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": [7.65, 19.5], "unit": "dimensionless"}

Answer: 7.65

Answer: 19.5

Prompt: A line passes through points (4, 50.1) and (6.25, 67.3125). 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.


Response:
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"}

Answer: inconsistent

Prompt: In sensor calibration case 238444, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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.

Answer: inconsistent


Response:
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_000700(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_000700"}

Answer: python_code

Prompt: Write a Python function center_values_000700(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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.

try:
    center_values_000700([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
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", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid laboratory survey records in release 252549, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 40.25^2 and multiply by 0.5 * 28.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 23085.8906, "unit": "J"}

Answer: 23085.8906

Prompt: A body of mass 28.5 kg moves at 40.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 40.25^2 and multiply by 0.5 * 28.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=37 degrees through the sine of 2 theta.
3. Substitute v=8.2 m/s and g=9.81 m/s^2.
Final: {"answer": 6.5887, "unit": "m"}

Answer: 6.5887

Prompt: A projectile is launched on level ground with no air resistance at speed 8.2 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=37 degrees through the sine of 2 theta.
Substitute v=8.2 m/s and g=9.81 m/s^2.

speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity


Response:
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 = 2.3 * 8.314 * 383 / 88.7.
Final: {"answer": 82.5682, "unit": "kPa"}

Answer: 82.5682

Prompt: An ideal gas sample has n=2.3 mol, T=383 K, and V=88.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 2.3 * 8.314 * 383 / 88.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1030 * 1.13 * 5.
Final: {"answer": 5819.5, "unit": "J"}

Answer: 5819.5

Prompt: A 1030 g sample has specific heat 1.13 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1030 * 1.13 * 5.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=856 mg, t=98 h, and T_half=80.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 368.1311, "unit": "mg"}

Answer: 368.1311

Prompt: A radioactive sample starts with 856 mg. Its half-life is 80.5 hours. How many mg remain after 98 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=856 mg, t=98 h, and T_half=80.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.38 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 197.5272, "unit": "g"}

Answer: 197.5272

Prompt: A sample contains 3.38 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 = 3.38 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0071, "unit": "state_units"}

Answer: 0.0071

Prompt: Use explicit Euler on dy/dt = -0.54 y with y(0)=9.5, step size h=0.95, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.1)=-8.13 and f(5.4)=20.68.
3. The interval width is 4.3.
Final: {"answer": 26.9825, "unit": "area_units"}

Answer: 26.9825

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+-15.5 from x=1.1 to x=5.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.1)=-8.13 and f(5.4)=20.68.
The interval width is 4.3.

(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 338.0 / 100.
Final: {"answer": 3.38, "unit": "m"}

Answer: 3.38

Prompt: Convert 338 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 338.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=128 degrees and keep the unit as newtons.
Final: {"answer": [-211.7875, 271.0757], "unit": "N"}

Answer: -211.7875

Answer: 271.0757

Prompt: A vector has magnitude 344 N at 128 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=128 degrees and keep the unit as newtons.


Response:
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": [-8.25, 16.5], "unit": "dimensionless"}

Answer: -8.25

Answer: 16.5

Prompt: A line passes through points (13, -90.75) and (19.75, -146.438). 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.


Response:
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"}

Answer: inconsistent

Prompt: In sensor calibration case 454466, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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.

Answer: inconsistent


Response:
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 threshold_flags_000718(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_000718"}

Answer: python_code

Prompt: Write a Python function threshold_flags_000718(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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.

assert threshold_flags_000718([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_000718([], 5) == []

assert threshold_flags_000718([-1, 0], 0) == [False, True]


Response:
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_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.08 and interior values [0.55, 1.85, -1.0], but gives no boundary values. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.25 kg and a = 10 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 242.5, "unit": "N"}

Answer: 242.5

Prompt: A cart has mass 24.25 kg and measured acceleration 10 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.25 kg and a = 10 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 15.75^2 and multiply by 0.5 * 15.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1879.0734, "unit": "J"}

Answer: 1879.0734

Prompt: A body of mass 15.15 kg moves at 15.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.75^2 and multiply by 0.5 * 15.15.
The unit kg*m^2/s^2 is one joule.


Response:
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 = 6 * 8.314 * 426 / 10.7.
Final: {"answer": 1986.0359, "unit": "kPa"}

Answer: 1986.0359

Prompt: An ideal gas sample has n=6 mol, T=426 K, and V=10.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 6 * 8.314 * 426 / 10.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 765 * 4.225 * 21.
Final: {"answer": 67874.625, "unit": "J"}

Answer: 67874.625

Prompt: A 765 g sample has specific heat 4.225 J/(g*K). How much heat is needed to raise its temperature by 21 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 765 * 4.225 * 21.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=179.9 V and R=131.6 ohm.
Final: {"answer": 245.9271, "unit": "W"}

Answer: 245.9271

Prompt: A resistor has resistance 131.6 ohm and voltage 179.9 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=179.9 V and R=131.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=892 mg, t=360 h, and T_half=110.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 93.2467, "unit": "mg"}

Answer: 93.2467

Prompt: A radioactive sample starts with 892 mg. Its half-life is 110.5 hours. How many mg remain after 360 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=892 mg, t=360 h, and T_half=110.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.84 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 33.1476, "unit": "g"}

Answer: 33.1476

Prompt: A sample contains 1.84 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 = 1.84 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1825 mL to 1.825 L.
3. Compute M = 1.045 / 1.825.
Final: {"answer": 0.5726, "unit": "mol/L"}

Answer: 0.5726

Prompt: A solution contains 1.045 mol of solute in 1825 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1825 mL to 1.825 L.
Compute M = 1.045 / 1.825.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.5)=0.7 and f(9.9)=7.42.
3. The interval width is 8.4.
Final: {"answer": 34.104, "unit": "area_units"}

Answer: 34.104

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.8x+-0.5 from x=1.5 to x=9.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.5)=0.7 and f(9.9)=7.42.
The interval width is 8.4.


Response:
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": [0.227, 0.468, -0.544], "unit": "temperature_units"}

Answer: 0.227

Answer: 0.468

Answer: -0.544

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.1, right=-0.75; current interior values are [0.55, -1.85, 1.85]. Use r=0.38. Return the next interior vector.

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.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 44331.0 / 1000.
Final: {"answer": 44.331, "unit": "kg"}

Answer: 44.331

Prompt: Convert 44331 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 44331.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=95 degrees and keep the unit as newtons.
Final: {"answer": [-31.2889, 357.6339], "unit": "N"}

Answer: -31.2889

Answer: 357.6339

Prompt: A vector has magnitude 359 N at 95 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=95 degrees and keep the unit as newtons.


Response:
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": [5.5, -12.5], "unit": "dimensionless"}

Answer: 5.5

Answer: -12.5

Prompt: A line passes through points (7.25, 27.375) and (17.25, 82.375). 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.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. density times acceleration times height gives kg/(m*s^2), or pascal
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In lab notebook case 948981, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
density times acceleration times height gives kg/(m*s^2), or pascal
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
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_000736(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000736"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000736(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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.

try:
    weighted_sum_000736([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
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": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=9.5 and h=0.8, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.65 kg and a = 4.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 82.955, "unit": "N"}

Answer: 82.955

Prompt: A cart has mass 17.65 kg and measured acceleration 4.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.65 kg and a = 4.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 18.95^2 and multiply by 0.5 * 8.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1481.2978, "unit": "J"}

Answer: 1481.2978

Prompt: A body of mass 8.25 kg moves at 18.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.95^2 and multiply by 0.5 * 8.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=77 degrees through the sine of 2 theta.
3. Substitute v=52.1 m/s and g=9.81 m/s^2.
Final: {"answer": 121.2965, "unit": "m"}

Answer: 121.2965

Prompt: A projectile is launched on level ground with no air resistance at speed 52.1 m/s and angle 77 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=77 degrees through the sine of 2 theta.
Substitute v=52.1 m/s and g=9.81 m/s^2.


Response:
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 = 3.56 * 8.314 * 267 / 103.1.
Final: {"answer": 76.6501, "unit": "kPa"}

Answer: 76.6501

Prompt: An ideal gas sample has n=3.56 mol, T=267 K, and V=103.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 3.56 * 8.314 * 267 / 103.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 715 * 3.62 * 12.
Final: {"answer": 31059.6, "unit": "J"}

Answer: 31059.6

Prompt: A 715 g sample has specific heat 3.62 J/(g*K). How much heat is needed to raise its temperature by 12 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 715 * 3.62 * 12.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.97 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 42.6897, "unit": "g"}

Answer: 42.6897

Prompt: A sample contains 0.97 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 = 0.97 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3625 mL to 3.625 L.
3. Compute M = 3.845 / 3.625.
Final: {"answer": 1.0607, "unit": "mol/L"}

Answer: 1.0607

Prompt: A solution contains 3.845 mol of solute in 3625 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3625 mL to 3.625 L.
Compute M = 3.845 / 3.625.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 2.1277, "unit": "state_units"}

Answer: 2.1277

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=17.5, step size h=0.65, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.2)=37.52 and f(10.9)=88.34.
3. The interval width is 7.7.
Final: {"answer": 484.561, "unit": "area_units"}

Answer: 484.561

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+16.4 from x=3.2 to x=10.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.2)=37.52 and f(10.9)=88.34.
The interval width is 7.7.


Response:
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=0.46 and add it to the current value.
Final: {"answer": [-0.114, 0.129, -0.525], "unit": "temperature_units"}

Answer: -0.114

Answer: 0.129

Answer: -0.525

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=-0.75; current interior values are [0.3, -0.4, 0.05]. Use r=0.46. Return the next interior vector.

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=0.46 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2642.0 / 100.
Final: {"answer": 26.42, "unit": "m"}

Answer: 26.42

Prompt: Convert 2642 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 2642.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=158 degrees and keep the unit as newtons.
Final: {"answer": [-41.2597, 16.67], "unit": "N"}

Answer: -41.2597

Answer: 16.67

Prompt: A vector has magnitude 44.5 N at 158 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=158 degrees and keep the unit as newtons.


Response:
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": [-7.1, -13.25], "unit": "dimensionless"}

Answer: -7.1

Answer: -13.25

Prompt: A line passes through points (4.5, -45.2) and (14, -112.65). 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.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. velocity times time gives distance, not acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In lab notebook case 486049, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity times time gives distance, not acceleration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
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_000754(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_000754"}

Answer: python_code

Prompt: Write a Python function safe_mean_000754(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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.

try:
    safe_mean_000754([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.55 kg and a = 13.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 285.645, "unit": "N"}

Answer: 285.645

Prompt: A cart has mass 20.55 kg and measured acceleration 13.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.55 kg and a = 13.9 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 17.55^2 and multiply by 0.5 * 10.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1547.7126, "unit": "J"}

Answer: 1547.7126

Prompt: A body of mass 10.05 kg moves at 17.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.55^2 and multiply by 0.5 * 10.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=30 degrees through the sine of 2 theta.
3. Substitute v=82.6 m/s and g=9.81 m/s^2.
Final: {"answer": 602.3123, "unit": "m"}

Answer: 602.3123

Prompt: A projectile is launched on level ground with no air resistance at speed 82.6 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=30 degrees through the sine of 2 theta.
Substitute v=82.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1075 * 4.055 * 5.
Final: {"answer": 21795.625, "unit": "J"}

Answer: 21795.625

Prompt: A 1075 g sample has specific heat 4.055 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1075 * 4.055 * 5.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=57.2 V and R=23 ohm.
Final: {"answer": 142.2539, "unit": "W"}

Answer: 142.2539

Prompt: A resistor has resistance 23 ohm and voltage 57.2 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=57.2 V and R=23 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=279 mg, t=189.5 h, and T_half=96 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 71.0205, "unit": "mg"}

Answer: 71.0205

Prompt: A radioactive sample starts with 279 mg. Its half-life is 96 hours. How many mg remain after 189.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=279 mg, t=189.5 h, and T_half=96 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.8 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1225.0608, "unit": "g"}

Answer: 1225.0608

Prompt: A sample contains 6.8 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 = 6.8 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2215 mL to 2.215 L.
3. Compute M = 3.9 / 2.215.
Final: {"answer": 1.7607, "unit": "mol/L"}

Answer: 1.7607

Prompt: A solution contains 3.9 mol of solute in 2215 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2215 mL to 2.215 L.
Compute M = 3.9 / 2.215.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.4)=-48.58 and f(15.3)=-114.91.
3. The interval width is 9.9.
Final: {"answer": -809.2755, "unit": "area_units"}

Answer: -809.2755

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+-12.4 from x=5.4 to x=15.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.4)=-48.58 and f(15.3)=-114.91.
The interval width is 9.9.


Response:
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": [0.7, 6.5], "unit": "dimensionless"}

Answer: 0.7

Answer: 6.5

Prompt: A line passes through points (-1.5, 5.45) and (0.75, 7.025). 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.


Response:
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"}

Answer: inconsistent

Prompt: In field worksheet case 447082, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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.

Answer: inconsistent


Response:
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": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each warehouse experiment record from batch 690725 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.6 kg and a = 5.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 70.04, "unit": "N"}

Answer: 70.04

Prompt: A cart has mass 13.6 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 13.6 kg and a = 5.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 33.65^2 and multiply by 0.5 * 3.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1924.9482, "unit": "J"}

Answer: 1924.9482

Prompt: A body of mass 3.4 kg moves at 33.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 33.65^2 and multiply by 0.5 * 3.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=21 degrees through the sine of 2 theta.
3. Substitute v=70 m/s and g=9.81 m/s^2.
Final: {"answer": 334.2243, "unit": "m"}

Answer: 334.2243

Prompt: A projectile is launched on level ground with no air resistance at speed 70 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=21 degrees through the sine of 2 theta.
Substitute v=70 m/s and g=9.81 m/s^2.


Response:
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 = 2.15 * 8.314 * 524 / 22.4.
Final: {"answer": 418.1497, "unit": "kPa"}

Answer: 418.1497

Prompt: An ideal gas sample has n=2.15 mol, T=524 K, and V=22.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 2.15 * 8.314 * 524 / 22.4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=11.1 V and R=46.2 ohm.
Final: {"answer": 2.6669, "unit": "W"}

Answer: 2.6669

Prompt: A resistor has resistance 46.2 ohm and voltage 11.1 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=11.1 V and R=46.2 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.75 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 452.91, "unit": "g"}

Answer: 452.91

Prompt: A sample contains 7.75 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 = 7.75 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2550 mL to 2.55 L.
3. Compute M = 4.92 / 2.55.
Final: {"answer": 1.9294, "unit": "mol/L"}

Answer: 1.9294

Prompt: A solution contains 4.92 mol of solute in 2550 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2550 mL to 2.55 L.
Compute M = 4.92 / 2.55.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 2.8415, "unit": "state_units"}

Answer: 2.8415

Prompt: Use explicit Euler on dy/dt = -0.12 y with y(0)=12, step size h=1.55, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6)=-19.5 and f(0)=-2.7.
3. The interval width is 6.
Final: {"answer": -66.6, "unit": "area_units"}

Answer: -66.6

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.8x+-2.7 from x=-6 to x=0. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6)=-19.5 and f(0)=-2.7.
The interval width is 6.


Response:
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=0.26 and add it to the current value.
Final: {"answer": [1.038, 1.574, 1.456], "unit": "temperature_units"}

Answer: 1.038

Answer: 1.574

Answer: 1.456

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.2, right=2.7; current interior values are [0.7, 2.9, 0.0]. Use r=0.26. Return the next interior vector.

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=0.26 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1736.0 / 100.
Final: {"answer": 17.36, "unit": "m"}

Answer: 17.36

Prompt: Convert 1736 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 1736.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=97 degrees and keep the unit as newtons.
Final: {"answer": [-27.969, 227.7893], "unit": "N"}

Answer: -27.969

Answer: 227.7893

Prompt: A vector has magnitude 229.5 N at 97 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=97 degrees and keep the unit as newtons.


Response:
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": [1.55, 14.25], "unit": "dimensionless"}

Answer: 1.55

Answer: 14.25

Prompt: A line passes through points (-5, 6.5) and (0.25, 14.6375). 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.


Response:
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"}

Answer: inconsistent

Prompt: In instrument manual case 799179, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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.

Answer: inconsistent


Response:
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_000790(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000790"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000790(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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.

try:
    weighted_sum_000790([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 42.6^2 and multiply by 0.5 * 2.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2359.188, "unit": "J"}

Answer: 2359.188

Prompt: A body of mass 2.6 kg moves at 42.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.6^2 and multiply by 0.5 * 2.6.
The unit kg*m^2/s^2 is one joule.


Response:
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=22.9 m/s and g=9.81 m/s^2.
Final: {"answer": 18.2833, "unit": "m"}

Answer: 18.2833

Prompt: A projectile is launched on level ground with no air resistance at speed 22.9 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=80 degrees through the sine of 2 theta.
Substitute v=22.9 m/s and g=9.81 m/s^2.


Response:
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 = 0.53 * 8.314 * 309 / 21.5.
Final: {"answer": 63.3295, "unit": "kPa"}

Answer: 63.3295

Prompt: An ideal gas sample has n=0.53 mol, T=309 K, and V=21.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 0.53 * 8.314 * 309 / 21.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1085 * 3.83 * 108.
Final: {"answer": 448799.4, "unit": "J"}

Answer: 448799.4

Prompt: A 1085 g sample has specific heat 3.83 J/(g*K). How much heat is needed to raise its temperature by 108 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1085 * 3.83 * 108.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=79.8 V and R=62.5 ohm.
Final: {"answer": 101.8886, "unit": "W"}

Answer: 101.8886

Prompt: A resistor has resistance 62.5 ohm and voltage 79.8 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=79.8 V and R=62.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=977 mg, t=201 h, and T_half=90 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 207.7755, "unit": "mg"}

Answer: 207.7755

Prompt: A radioactive sample starts with 977 mg. Its half-life is 90 hours. How many mg remain after 201 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=977 mg, t=201 h, and T_half=90 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2150 mL to 2.15 L.
3. Compute M = 1.59 / 2.15.
Final: {"answer": 0.7395, "unit": "mol/L"}

Answer: 0.7395

Prompt: A solution contains 1.59 mol of solute in 2150 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2150 mL to 2.15 L.
Compute M = 1.59 / 2.15.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.1038, "unit": "state_units"}

Answer: 0.1038

Prompt: Use explicit Euler on dy/dt = -0.32 y with y(0)=22.5, step size h=1.85, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1)=17.6 and f(2.1)=24.97.
3. The interval width is 1.1.
Final: {"answer": 23.4135, "unit": "area_units"}

Answer: 23.4135

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+10.9 from x=1 to x=2.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1)=17.6 and f(2.1)=24.97.
The interval width is 1.1.


Response:
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": [0.25, -0.4, 0.68], "unit": "temperature_units"}

Answer: 0.25

Answer: -0.4

Answer: 0.68

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.25, right=1; current interior values are [-1.05, 0.9, -0.4]. Use r=0.4. Return the next interior vector.

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.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=1 degrees and keep the unit as newtons.
Final: {"answer": [64.9901, 1.1344], "unit": "N"}

Answer: 64.9901

Answer: 1.1344

Prompt: A vector has magnitude 65 N at 1 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=1 degrees and keep the unit as newtons.


Response:
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": [7.4, 14.5], "unit": "dimensionless"}

Answer: 7.4

Answer: 14.5

Prompt: A line passes through points (-3, -7.7) and (9, 81.1). 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.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 593813, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
volt squared divided by ohm is watt
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
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_000808(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_000808"}

Answer: python_code

Prompt: Write a Python function normalize_000808(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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.

out = normalize_000808([2, 3, 5]); assert len(out) == 3

try:
    normalize_000808([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: launch_angle_or_vertical_velocity.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 38.8 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: launch_angle_or_vertical_velocity.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.4 kg and a = 10.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 241.92, "unit": "N"}

Answer: 241.92

Prompt: A cart has mass 22.4 kg and measured acceleration 10.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.4 kg and a = 10.8 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.75^2 and multiply by 0.5 * 24.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 23638.6719, "unit": "J"}

Answer: 23638.6719

Prompt: A body of mass 24.7 kg moves at 43.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.75^2 and multiply by 0.5 * 24.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=43 degrees through the sine of 2 theta.
3. Substitute v=35.4 m/s and g=9.81 m/s^2.
Final: {"answer": 127.4319, "unit": "m"}

Answer: 127.4319

Prompt: A projectile is launched on level ground with no air resistance at speed 35.4 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=43 degrees through the sine of 2 theta.
Substitute v=35.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=92.6 V and R=60.7 ohm.
Final: {"answer": 141.2646, "unit": "W"}

Answer: 141.2646

Prompt: A resistor has resistance 60.7 ohm and voltage 92.6 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=92.6 V and R=60.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=555.5 mg, t=23.5 h, and T_half=2 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.1613, "unit": "mg"}

Answer: 0.1613

Prompt: A radioactive sample starts with 555.5 mg. Its half-life is 2 hours. How many mg remain after 23.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=555.5 mg, t=23.5 h, and T_half=2 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.51 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 632.3476, "unit": "g"}

Answer: 632.3476

Prompt: A sample contains 3.51 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 = 3.51 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.51 y with y(0)=9.5, step size h=1.75, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2523.5 / 100.
Final: {"answer": 25.235, "unit": "m"}

Answer: 25.235

Prompt: Convert 2523.5 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 2523.5 / 100.


Response:
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": [-0.05, 4.75], "unit": "dimensionless"}

Answer: -0.05

Answer: 4.75

Prompt: A line passes through points (4, 4.55) and (16, 3.95). 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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.7 kg and a = 3.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 85.125, "unit": "N"}

Answer: 85.125

Prompt: A cart has mass 22.7 kg and measured acceleration 3.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.7 kg and a = 3.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 24.6^2 and multiply by 0.5 * 25.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7776.306, "unit": "J"}

Answer: 7776.306

Prompt: A body of mass 25.7 kg moves at 24.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24.6^2 and multiply by 0.5 * 25.7.
The unit kg*m^2/s^2 is one joule.


Response:
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 = 3.47 * 8.314 * 293 / 17.1.
Final: {"answer": 494.3232, "unit": "kPa"}

Answer: 494.3232

Prompt: An ideal gas sample has n=3.47 mol, T=293 K, and V=17.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 3.47 * 8.314 * 293 / 17.1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=108 V and R=57.4 ohm.
Final: {"answer": 203.2056, "unit": "W"}

Answer: 203.2056

Prompt: A resistor has resistance 57.4 ohm and voltage 108 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=108 V and R=57.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=26.5 mg, t=110 h, and T_half=24 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.1054, "unit": "mg"}

Answer: 1.1054

Prompt: A radioactive sample starts with 26.5 mg. Its half-life is 24 hours. How many mg remain after 110 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=26.5 mg, t=110 h, and T_half=24 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.12 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 65.4528, "unit": "g"}

Answer: 65.4528

Prompt: A sample contains 1.12 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 = 1.12 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2565 mL to 2.565 L.
3. Compute M = 4.375 / 2.565.
Final: {"answer": 1.7057, "unit": "mol/L"}

Answer: 1.7057

Prompt: A solution contains 4.375 mol of solute in 2565 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2565 mL to 2.565 L.
Compute M = 4.375 / 2.565.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.8804, "unit": "state_units"}

Answer: 0.8804

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=1, step size h=0.7, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6)=9.4 and f(2.7)=5.92.
3. The interval width is 8.7.
Final: {"answer": 66.642, "unit": "area_units"}

Answer: 66.642

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+7 from x=-6 to x=2.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6)=9.4 and f(2.7)=5.92.
The interval width is 8.7.


Response:
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": [0.26, 0.56, -0.08], "unit": "temperature_units"}

Answer: 0.26

Answer: 0.56

Answer: -0.08

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.45, right=0.8; current interior values are [0.4, -2.0, 2.0]. Use r=0.4. Return the next interior vector.

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.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=63 degrees and keep the unit as newtons.
Final: {"answer": [182.2772, 357.7391], "unit": "N"}

Answer: 182.2772

Answer: 357.7391

Prompt: A vector has magnitude 401.5 N at 63 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=63 degrees and keep the unit as newtons.


Response:
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": [5.15, -10.25], "unit": "dimensionless"}

Answer: 5.15

Answer: -10.25

Prompt: A line passes through points (1.5, -2.525) and (2.25, 1.3375). 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.


Response:
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"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=3.51 mol and T=531 K, but does not give volume. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.05 kg and a = 0.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 0.2625, "unit": "N"}

Answer: 0.2625

Prompt: A cart has mass 1.05 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.05 kg and a = 0.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 32.45^2 and multiply by 0.5 * 27.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 14689.3849, "unit": "J"}

Answer: 14689.3849

Prompt: A body of mass 27.9 kg moves at 32.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.45^2 and multiply by 0.5 * 27.9.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=48 degrees through the sine of 2 theta.
3. Substitute v=71.8 m/s and g=9.81 m/s^2.
Final: {"answer": 522.6299, "unit": "m"}

Answer: 522.6299

Prompt: A projectile is launched on level ground with no air resistance at speed 71.8 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=48 degrees through the sine of 2 theta.
Substitute v=71.8 m/s and g=9.81 m/s^2.


Response:
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 = 4.78 * 8.314 * 359 / 117.5.
Final: {"answer": 121.4212, "unit": "kPa"}

Answer: 121.4212

Prompt: An ideal gas sample has n=4.78 mol, T=359 K, and V=117.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 4.78 * 8.314 * 359 / 117.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 540 * 0.525 * 81.
Final: {"answer": 22963.5, "unit": "J"}

Answer: 22963.5

Prompt: A 540 g sample has specific heat 0.525 J/(g*K). How much heat is needed to raise its temperature by 81 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 540 * 0.525 * 81.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=195.3 V and R=173.9 ohm.
Final: {"answer": 219.3335, "unit": "W"}

Answer: 219.3335

Prompt: A resistor has resistance 173.9 ohm and voltage 195.3 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=195.3 V and R=173.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=598 mg, t=302 h, and T_half=6 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 598 mg. Its half-life is 6 hours. How many mg remain after 302 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=598 mg, t=302 h, and T_half=6 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.12 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 381.9307, "unit": "g"}

Answer: 381.9307

Prompt: A sample contains 2.12 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 = 2.12 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4160 mL to 4.16 L.
3. Compute M = 4.085 / 4.16.
Final: {"answer": 0.982, "unit": "mol/L"}

Answer: 0.982

Prompt: A solution contains 4.085 mol of solute in 4160 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4160 mL to 4.16 L.
Compute M = 4.085 / 4.16.


Response:
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 12 steps and round the final state.
Final: {"answer": 14.3235, "unit": "state_units"}

Answer: 14.3235

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=53.5, step size h=1.3, for 12 steps. What is y after the final step?

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 12 steps and round the final state.


Response:
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"}

Answer: inconsistent

Prompt: In instrument manual case 222640, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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.

Answer: inconsistent


Response:
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_000862(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000862"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000862(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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.

try:
    weighted_sum_000862([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: launch_angle_or_vertical_velocity.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 65 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: launch_angle_or_vertical_velocity.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.75 kg and a = 1.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 14.1375, "unit": "N"}

Answer: 14.1375

Prompt: A cart has mass 9.75 kg and measured acceleration 1.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.75 kg and a = 1.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 3.3^2 and multiply by 0.5 * 25.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 136.3972, "unit": "J"}

Answer: 136.3972

Prompt: A body of mass 25.05 kg moves at 3.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.3^2 and multiply by 0.5 * 25.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=21 degrees through the sine of 2 theta.
3. Substitute v=18.8 m/s and g=9.81 m/s^2.
Final: {"answer": 24.1078, "unit": "m"}

Answer: 24.1078

Prompt: A projectile is launched on level ground with no air resistance at speed 18.8 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=21 degrees through the sine of 2 theta.
Substitute v=18.8 m/s and g=9.81 m/s^2.


Response:
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 = 3.97 * 8.314 * 256 / 72.2.
Final: {"answer": 117.0316, "unit": "kPa"}

Answer: 117.0316

Prompt: An ideal gas sample has n=3.97 mol, T=256 K, and V=72.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 3.97 * 8.314 * 256 / 72.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 640 * 0.81 * 80.
Final: {"answer": 41472.0, "unit": "J"}

Answer: 41472.0

Prompt: A 640 g sample has specific heat 0.81 J/(g*K). How much heat is needed to raise its temperature by 80 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 640 * 0.81 * 80.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=56.1 V and R=124.8 ohm.
Final: {"answer": 25.218, "unit": "W"}

Answer: 25.218

Prompt: A resistor has resistance 124.8 ohm and voltage 56.1 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=56.1 V and R=124.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=176 mg, t=23.5 h, and T_half=25.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 92.9165, "unit": "mg"}

Answer: 92.9165

Prompt: A radioactive sample starts with 176 mg. Its half-life is 25.5 hours. How many mg remain after 23.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=176 mg, t=23.5 h, and T_half=25.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.93 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 106.8289, "unit": "g"}

Answer: 106.8289

Prompt: A sample contains 5.93 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 = 5.93 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 420 mL to 0.42 L.
3. Compute M = 0.365 / 0.42.
Final: {"answer": 0.869, "unit": "mol/L"}

Answer: 0.869

Prompt: A solution contains 0.365 mol of solute in 420 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 420 mL to 0.42 L.
Compute M = 0.365 / 0.42.


Response:
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": 0.1137, "unit": "state_units"}

Answer: 0.1137

Prompt: Use explicit Euler on dy/dt = -0.94 y with y(0)=14, step size h=0.85, for 3 steps. What is y after the final step?

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.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.3)=-8.52 and f(-1.6)=-10.74.
3. The interval width is 3.7.
Final: {"answer": -35.631, "unit": "area_units"}

Answer: -35.631

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+-11.7 from x=-5.3 to x=-1.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.3)=-8.52 and f(-1.6)=-10.74.
The interval width is 3.7.


Response:
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": [-0.782, -0.568, -0.452], "unit": "temperature_units"}

Answer: -0.782

Answer: -0.568

Answer: -0.452

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-0.1; current interior values are [-2.0, 1.0, -1.6]. Use r=0.28. Return the next interior vector.

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.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1313.0 / 100.
Final: {"answer": 13.13, "unit": "m"}

Answer: 13.13

Prompt: Convert 1313 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 1313.0 / 100.


Response:
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": [3.2, -0.25], "unit": "dimensionless"}

Answer: 3.2

Answer: -0.25

Prompt: A line passes through points (-4.5, -14.65) and (8.5, 26.95). 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.


Response:
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"}

Answer: inconsistent

Prompt: In instrument manual case 691479, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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.

Answer: inconsistent


Response:
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_000880(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000880"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000880(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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.

try:
    weighted_sum_000880([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
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": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each billing experiment record from batch 203867 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.3 kg and a = 0.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 13.38, "unit": "N"}

Answer: 13.38

Prompt: A cart has mass 22.3 kg and measured acceleration 0.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.3 kg and a = 0.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
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=49.2 m/s and g=9.81 m/s^2.
Final: {"answer": 246.7523, "unit": "m"}

Answer: 246.7523

Prompt: A projectile is launched on level ground with no air resistance at speed 49.2 m/s and angle 45 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=45 degrees through the sine of 2 theta.
Substitute v=49.2 m/s and g=9.81 m/s^2.


Response:
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 = 2.39 * 8.314 * 431 / 89.3.
Final: {"answer": 95.9033, "unit": "kPa"}

Answer: 95.9033

Prompt: An ideal gas sample has n=2.39 mol, T=431 K, and V=89.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

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 = 2.39 * 8.314 * 431 / 89.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1420 * 3.255 * 112.
Final: {"answer": 517675.2, "unit": "J"}

Answer: 517675.2

Prompt: A 1420 g sample has specific heat 3.255 J/(g*K). How much heat is needed to raise its temperature by 112 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1420 * 3.255 * 112.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=9.1 V and R=198.5 ohm.
Final: {"answer": 0.4172, "unit": "W"}

Answer: 0.4172

Prompt: A resistor has resistance 198.5 ohm and voltage 9.1 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=9.1 V and R=198.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=403.5 mg, t=143.5 h, and T_half=96 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 143.1747, "unit": "mg"}

Answer: 143.1747

Prompt: A radioactive sample starts with 403.5 mg. Its half-life is 96 hours. How many mg remain after 143.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=403.5 mg, t=143.5 h, and T_half=96 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4525 mL to 4.525 L.
3. Compute M = 0.295 / 4.525.
Final: {"answer": 0.0652, "unit": "mol/L"}

Answer: 0.0652

Prompt: A solution contains 0.295 mol of solute in 4525 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4525 mL to 4.525 L.
Compute M = 0.295 / 4.525.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": -0.1421, "unit": "state_units"}

Answer: -0.1421

Prompt: Use explicit Euler on dy/dt = -0.96 y with y(0)=44.5, step size h=1.5, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
Apply that update for 7 steps and round the final state.


Response:
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=0.04 and add it to the current value.
Final: {"answer": [2.434, -1.506, 0.83], "unit": "temperature_units"}

Answer: 2.434

Answer: -1.506

Answer: 0.83

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.55, right=-1.6; current interior values are [2.7, -1.8, 1.05]. Use r=0.04. Return the next interior vector.

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=0.04 and add it to the current value.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. lever arm times force has torque dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In quality-control check case 689724, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
lever arm times force has torque dimensions
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
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_000898(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_000898"}

Answer: python_code

Prompt: Write a Python function safe_mean_000898(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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.

try:
    safe_mean_000898([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
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", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a allocation scoring problem with 2753 items and budget 91755, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.85 kg and a = 13.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 297.16, "unit": "N"}

Answer: 297.16

Prompt: A cart has mass 21.85 kg and measured acceleration 13.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.85 kg and a = 13.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=39 degrees through the sine of 2 theta.
3. Substitute v=43.6 m/s and g=9.81 m/s^2.
Final: {"answer": 189.5433, "unit": "m"}

Answer: 189.5433

Prompt: A projectile is launched on level ground with no air resistance at speed 43.6 m/s and angle 39 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=39 degrees through the sine of 2 theta.
Substitute v=43.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1260 * 4.235 * 12.
Final: {"answer": 64033.2, "unit": "J"}

Answer: 64033.2

Prompt: A 1260 g sample has specific heat 4.235 J/(g*K). How much heat is needed to raise its temperature by 12 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1260 * 4.235 * 12.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=141.8 V and R=135.9 ohm.
Final: {"answer": 147.9561, "unit": "W"}

Answer: 147.9561

Prompt: A resistor has resistance 135.9 ohm and voltage 141.8 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=141.8 V and R=135.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=21.5 mg, t=67.5 h, and T_half=108.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 13.9689, "unit": "mg"}

Answer: 13.9689

Prompt: A radioactive sample starts with 21.5 mg. Its half-life is 108.5 hours. How many mg remain after 67.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=21.5 mg, t=67.5 h, and T_half=108.5 h.
The remaining amount has the same mass unit as the initial amount.