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 = 0.25 * 8.314 * 473 / 54.9.
Final: {"answer": 17.9077, "unit": "kPa"}

Answer: 17.9077

Prompt: An ideal gas sample has n=0.25 mol, T=473 K, and V=54.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.25 * 8.314 * 473 / 54.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1890 * 2.415 * 6.
Final: {"answer": 27386.1, "unit": "J"}

Answer: 27386.1

Prompt: A 1890 g sample has specific heat 2.415 J/(g*K). How much heat is needed to raise its temperature by 6 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1890 * 2.415 * 6.


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=190.4 V and R=112.9 ohm.
Final: {"answer": 321.0997, "unit": "W"}

Answer: 321.0997

Prompt: A resistor has resistance 112.9 ohm and voltage 190.4 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=190.4 V and R=112.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=827.5 mg, t=19.5 h, and T_half=50.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 633.1822, "unit": "mg"}

Answer: 633.1822

Prompt: A radioactive sample starts with 827.5 mg. Its half-life is 50.5 hours. How many mg remain after 19.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=827.5 mg, t=19.5 h, and T_half=50.5 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 = 1.36 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 59.8536, "unit": "g"}

Answer: 59.8536

Prompt: A sample contains 1.36 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 = 1.36 mol * 44.01 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) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 6.7712, "unit": "state_units"}

Answer: 6.7712

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=10.5, step size h=1.05, for 5 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 5 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 3819.5 / 100.
Final: {"answer": 38.195, "unit": "m"}

Answer: 38.195

Prompt: Convert 3819.5 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 3819.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=312 degrees and keep the unit as newtons.
Final: {"answer": [53.5304, -59.4516], "unit": "N"}

Answer: 53.5304

Answer: -59.4516

Prompt: A vector has magnitude 80 N at 312 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=312 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": [0.4, -5.25], "unit": "dimensionless"}

Answer: 0.4

Answer: -5.25

Prompt: A line passes through points (-8.25, -8.55) and (0.25, -5.15). 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 quality-control check case 665462, 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. 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 mobile clinical records in release 776263, 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. Use Newton's second law F = m a.
2. Substitute m = 11.45 kg and a = 0.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 2.8625, "unit": "N"}

Answer: 2.8625

Prompt: A cart has mass 11.45 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 = 11.45 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 = 11.25^2 and multiply by 0.5 * 19.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1252.9688, "unit": "J"}

Answer: 1252.9688

Prompt: A body of mass 19.8 kg moves at 11.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.25^2 and multiply by 0.5 * 19.8.
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 = 4.42 * 8.314 * 377 / 70.2.
Final: {"answer": 197.3497, "unit": "kPa"}

Answer: 197.3497

Prompt: An ideal gas sample has n=4.42 mol, T=377 K, and V=70.2 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 = 4.42 * 8.314 * 377 / 70.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 470 * 1.65 * 23.
Final: {"answer": 17836.5, "unit": "J"}

Answer: 17836.5

Prompt: A 470 g sample has specific heat 1.65 J/(g*K). How much heat is needed to raise its temperature by 23 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 470 * 1.65 * 23.


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=209 V and R=124 ohm.
Final: {"answer": 352.2661, "unit": "W"}

Answer: 352.2661

Prompt: A resistor has resistance 124 ohm and voltage 209 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=209 V and R=124 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=778.5 mg, t=330 h, and T_half=37.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.7466, "unit": "mg"}

Answer: 1.7466

Prompt: A radioactive sample starts with 778.5 mg. Its half-life is 37.5 hours. How many mg remain after 330 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=778.5 mg, t=330 h, and T_half=37.5 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 = 4.51 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 263.5644, "unit": "g"}

Answer: 263.5644

Prompt: A sample contains 4.51 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 = 4.51 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 4265 mL to 4.265 L.
3. Compute M = 0.685 / 4.265.
Final: {"answer": 0.1606, "unit": "mol/L"}

Answer: 0.1606

Prompt: A solution contains 0.685 mol of solute in 4265 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4265 mL to 4.265 L.
Compute M = 0.685 / 4.265.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.1324, "unit": "state_units"}

Answer: 0.1324

Prompt: Use explicit Euler on dy/dt = -0.28 y with y(0)=2, step size h=1.3, 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) = -0.28 y, so each step multiplies y by 1 - h*0.28.
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(-5.3)=17.76 and f(-0.6)=2.72.
3. The interval width is 4.7.
Final: {"answer": 48.128, "unit": "area_units"}

Answer: 48.128

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.2x+0.8 from x=-5.3 to x=-0.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.3)=17.76 and f(-0.6)=2.72.
The interval width is 4.7.

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


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": [0.926, -0.388, 1.472], "unit": "temperature_units"}

Answer: 0.926

Answer: -0.388

Answer: 1.472

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=0.5; current interior values are [1.55, -1.5, 2.4]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=340 degrees and keep the unit as newtons.
Final: {"answer": [77.9945, -28.3877], "unit": "N"}

Answer: 77.9945

Answer: -28.3877

Prompt: A vector has magnitude 83 N at 340 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=340 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": [7.15, 14.25], "unit": "dimensionless"}

Answer: 7.15

Answer: 14.25

Prompt: A line passes through points (-5.5, -25.075) and (4.25, 44.6375). 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. 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 field worksheet case 486336, 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 running_total_007846(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007846"}

Answer: python_code

Prompt: Write a Python function running_total_007846(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.


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=1.29 mol and T=519 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 = 8.2 kg and a = 13.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 108.65, "unit": "N"}

Answer: 108.65

Prompt: A cart has mass 8.2 kg and measured acceleration 13.25 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 = 8.2 kg and a = 13.25 m/s^2.
The unit kg*m/s^2 is one newton.


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 = 1.02 * 8.314 * 547 / 108.2.
Final: {"answer": 42.8717, "unit": "kPa"}

Answer: 42.8717

Prompt: An ideal gas sample has n=1.02 mol, T=547 K, and V=108.2 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 = 1.02 * 8.314 * 547 / 108.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 240 * 2.605 * 92.
Final: {"answer": 57518.4, "unit": "J"}

Answer: 57518.4

Prompt: A 240 g sample has specific heat 2.605 J/(g*K). How much heat is needed to raise its temperature by 92 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 240 * 2.605 * 92.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=964.5 mg, t=357.5 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 964.5 mg. Its half-life is 6 hours. How many mg remain after 357.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=964.5 mg, t=357.5 h, and T_half=6 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 1700 mL to 1.7 L.
3. Compute M = 3.39 / 1.7.
Final: {"answer": 1.9941, "unit": "mol/L"}

Answer: 1.9941

Prompt: A solution contains 3.39 mol of solute in 1700 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1700 mL to 1.7 L.
Compute M = 3.39 / 1.7.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 20.9128, "unit": "state_units"}

Answer: 20.9128

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=73.5, step size h=0.9, 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) = -0.21 y, so each step multiplies y by 1 - h*0.21.
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(-4)=23.3 and f(-0.6)=18.2.
3. The interval width is 3.4.
Final: {"answer": 70.55, "unit": "area_units"}

Answer: 70.55

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+17.3 from x=-4 to x=-0.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4)=23.3 and f(-0.6)=18.2.
The interval width is 3.4.


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=0.4 and add it to the current value.
Final: {"answer": [-1.07, 0.67, 0.0], "unit": "temperature_units"}

Answer: -1.07

Answer: 0.67

Answer: 0.0

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.35, right=1.25; current interior values are [1.25, -1.95, 1.4]. 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. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4918.5 / 100.
Final: {"answer": 49.185, "unit": "m"}

Answer: 49.185

Prompt: Convert 4918.5 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 4918.5 / 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": [-4.1, 10.75], "unit": "dimensionless"}

Answer: -4.1

Answer: 10.75

Prompt: A line passes through points (-1, 14.85) and (2, 2.55). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


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

Answer: consistent

Prompt: In sensor calibration case 453055, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
mass times acceleration has newton dimensions
The equation is valid only if both sides have identical dimensions.

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_007864(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_007864"}

Answer: python_code

Prompt: Write a Python function weighted_sum_007864(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_007864([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: 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 registry clinical records in release 169886, 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. Use Newton's second law F = m a.
2. Substitute m = 1.6 kg and a = 15.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 25.36, "unit": "N"}

Answer: 25.36

Prompt: A cart has mass 1.6 kg and measured acceleration 15.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.6 kg and a = 15.85 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 = 12.9^2 and multiply by 0.5 * 26.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2213.253, "unit": "J"}

Answer: 2213.253

Prompt: A body of mass 26.6 kg moves at 12.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.9^2 and multiply by 0.5 * 26.6.
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=18 degrees through the sine of 2 theta.
3. Substitute v=41.3 m/s and g=9.81 m/s^2.
Final: {"answer": 102.1997, "unit": "m"}

Answer: 102.1997

Prompt: A projectile is launched on level ground with no air resistance at speed 41.3 m/s and angle 18 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=18 degrees through the sine of 2 theta.
Substitute v=41.3 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 = 1.73 * 8.314 * 615 / 94.9.
Final: {"answer": 93.2105, "unit": "kPa"}

Answer: 93.2105

Prompt: An ideal gas sample has n=1.73 mol, T=615 K, and V=94.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.73 * 8.314 * 615 / 94.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 385 * 4.72 * 41.
Final: {"answer": 74505.2, "unit": "J"}

Answer: 74505.2

Prompt: A 385 g sample has specific heat 4.72 J/(g*K). How much heat is needed to raise its temperature by 41 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 385 * 4.72 * 41.


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=12.5 V and R=124 ohm.
Final: {"answer": 1.2601, "unit": "W"}

Answer: 1.2601

Prompt: A resistor has resistance 124 ohm and voltage 12.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=12.5 V and R=124 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=398 mg, t=355.5 h, and T_half=23.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0111, "unit": "mg"}

Answer: 0.0111

Prompt: A radioactive sample starts with 398 mg. Its half-life is 23.5 hours. How many mg remain after 355.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=398 mg, t=355.5 h, and T_half=23.5 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 = 5.65 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 565.4916, "unit": "g"}

Answer: 565.4916

Prompt: A sample contains 5.65 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 = 5.65 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 690 mL to 0.69 L.
3. Compute M = 3.085 / 0.69.
Final: {"answer": 4.471, "unit": "mol/L"}

Answer: 4.471

Prompt: A solution contains 3.085 mol of solute in 690 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 690 mL to 0.69 L.
Compute M = 3.085 / 0.69.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.9)=2.15 and f(9.6)=41.3.
3. The interval width is 8.7.
Final: {"answer": 189.0075, "unit": "area_units"}

Answer: 189.0075

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.5x+-1.9 from x=0.9 to x=9.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.9)=2.15 and f(9.6)=41.3.
The interval width is 8.7.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=96 degrees and keep the unit as newtons.
Final: {"answer": [-32.1948, 306.3127], "unit": "N"}

Answer: -32.1948

Answer: 306.3127

Prompt: A vector has magnitude 308 N at 96 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=96 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": [-9.8, -12.5], "unit": "dimensionless"}

Answer: -9.8

Answer: -12.5

Prompt: A line passes through points (-14, 124.7) and (-12, 105.1). 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. 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
import math

def unit_vector_007882(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_007882"}

Answer: python_code

Prompt: Write a Python function unit_vector_007882(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. 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:
    unit_vector_007882(0, 0)
    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 crop records in release 226488, 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 = 22.75^2 and multiply by 0.5 * 1.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 349.3547, "unit": "J"}

Answer: 349.3547

Prompt: A body of mass 1.35 kg moves at 22.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 22.75^2 and multiply by 0.5 * 1.35.
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=33 degrees through the sine of 2 theta.
3. Substitute v=8.6 m/s and g=9.81 m/s^2.
Final: {"answer": 6.8874, "unit": "m"}

Answer: 6.8874

Prompt: A projectile is launched on level ground with no air resistance at speed 8.6 m/s and angle 33 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=33 degrees through the sine of 2 theta.
Substitute v=8.6 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 = 5.11 * 8.314 * 256 / 101.9.
Final: {"answer": 106.7325, "unit": "kPa"}

Answer: 106.7325

Prompt: An ideal gas sample has n=5.11 mol, T=256 K, and V=101.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.11 * 8.314 * 256 / 101.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 370 * 2.04 * 29.
Final: {"answer": 21889.2, "unit": "J"}

Answer: 21889.2

Prompt: A 370 g sample has specific heat 2.04 J/(g*K). How much heat is needed to raise its temperature by 29 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 370 * 2.04 * 29.


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=239.8 V and R=67.9 ohm.
Final: {"answer": 846.8931, "unit": "W"}

Answer: 846.8931

Prompt: A resistor has resistance 67.9 ohm and voltage 239.8 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=239.8 V and R=67.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=336 mg, t=252.5 h, and T_half=88 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 45.9821, "unit": "mg"}

Answer: 45.9821

Prompt: A radioactive sample starts with 336 mg. Its half-life is 88 hours. How many mg remain after 252.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=336 mg, t=252.5 h, and T_half=88 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 = 5.6 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 246.456, "unit": "g"}

Answer: 246.456

Prompt: A sample contains 5.6 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 = 5.6 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 2075 mL to 2.075 L.
3. Compute M = 0.455 / 2.075.
Final: {"answer": 0.2193, "unit": "mol/L"}

Answer: 0.2193

Prompt: A solution contains 0.455 mol of solute in 2075 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2075 mL to 2.075 L.
Compute M = 0.455 / 2.075.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.73 y with y(0)=66.5, step size h=1.35, 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) = -0.73 y, so each step multiplies y by 1 - h*0.73.
Apply that update for 12 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(-8.1)=25.22 and f(-4.3)=16.86.
3. The interval width is 3.8.
Final: {"answer": 79.952, "unit": "area_units"}

Answer: 79.952

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+7.4 from x=-8.1 to x=-4.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.1)=25.22 and f(-4.3)=16.86.
The interval width is 3.8.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 4485.0 / 1000.
Final: {"answer": 4.485, "unit": "kg"}

Answer: 4.485

Prompt: Convert 4485 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 4485.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=10 degrees and keep the unit as newtons.
Final: {"answer": [399.8319, 70.5012], "unit": "N"}

Answer: 399.8319

Answer: 70.5012

Prompt: A vector has magnitude 406 N at 10 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=10 degrees and keep the unit as newtons.


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 quality-control check case 69127, 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. 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 253 items and budget 85325, 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 = 12.3 kg and a = 14.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 180.195, "unit": "N"}

Answer: 180.195

Prompt: A cart has mass 12.3 kg and measured acceleration 14.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 12.3 kg and a = 14.65 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 = 7.85^2 and multiply by 0.5 * 24.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 757.9567, "unit": "J"}

Answer: 757.9567

Prompt: A body of mass 24.6 kg moves at 7.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.85^2 and multiply by 0.5 * 24.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 825 * 1.015 * 89.
Final: {"answer": 74526.375, "unit": "J"}

Answer: 74526.375

Prompt: A 825 g sample has specific heat 1.015 J/(g*K). How much heat is needed to raise its temperature by 89 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 825 * 1.015 * 89.


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=189 V and R=48.9 ohm.
Final: {"answer": 730.4908, "unit": "W"}

Answer: 730.4908

Prompt: A resistor has resistance 48.9 ohm and voltage 189 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=189 V and R=48.9 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4550 mL to 4.55 L.
3. Compute M = 1.145 / 4.55.
Final: {"answer": 0.2516, "unit": "mol/L"}

Answer: 0.2516

Prompt: A solution contains 1.145 mol of solute in 4550 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4550 mL to 4.55 L.
Compute M = 1.145 / 4.55.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.56 y with y(0)=12.5, step size h=1.65, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.
Apply that update for 8 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(0.4)=21.62 and f(5.6)=59.58.
3. The interval width is 5.2.
Final: {"answer": 211.12, "unit": "area_units"}

Answer: 211.12

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+18.7 from x=0.4 to x=5.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.4)=21.62 and f(5.6)=59.58.
The interval width is 5.2.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=118 degrees and keep the unit as newtons.
Final: {"answer": [-53.0503, 99.7731], "unit": "N"}

Answer: -53.0503

Answer: 99.7731

Prompt: A vector has magnitude 113 N at 118 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=118 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": [8.95, -17.25], "unit": "dimensionless"}

Answer: 8.95

Answer: -17.25

Prompt: A line passes through points (-2.5, -39.625) and (7.75, 52.1125). 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 777754, 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 running_total_007918(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007918"}

Answer: python_code

Prompt: Write a Python function running_total_007918(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.


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 field crop records in release 575884, 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. Use Newton's second law F = m a.
2. Substitute m = 24.8 kg and a = 5.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 126.48, "unit": "N"}

Answer: 126.48

Prompt: A cart has mass 24.8 kg and measured acceleration 5.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.8 kg and a = 5.1 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 = 32.95^2 and multiply by 0.5 * 18.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10097.0333, "unit": "J"}

Answer: 10097.0333

Prompt: A body of mass 18.6 kg moves at 32.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.95^2 and multiply by 0.5 * 18.6.
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=20 degrees through the sine of 2 theta.
3. Substitute v=25.9 m/s and g=9.81 m/s^2.
Final: {"answer": 43.954, "unit": "m"}

Answer: 43.954

Prompt: A projectile is launched on level ground with no air resistance at speed 25.9 m/s and angle 20 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=20 degrees through the sine of 2 theta.
Substitute v=25.9 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 = 4.9 * 8.314 * 458 / 97.8.
Final: {"answer": 190.7799, "unit": "kPa"}

Answer: 190.7799

Prompt: An ideal gas sample has n=4.9 mol, T=458 K, and V=97.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.9 * 8.314 * 458 / 97.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1880 * 2.255 * 71.
Final: {"answer": 300997.4, "unit": "J"}

Answer: 300997.4

Prompt: A 1880 g sample has specific heat 2.255 J/(g*K). How much heat is needed to raise its temperature by 71 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1880 * 2.255 * 71.


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=130.2 V and R=43.9 ohm.
Final: {"answer": 386.1513, "unit": "W"}

Answer: 386.1513

Prompt: A resistor has resistance 43.9 ohm and voltage 130.2 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=130.2 V and R=43.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=100.5 mg, t=9.5 h, and T_half=4 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 19.374, "unit": "mg"}

Answer: 19.374

Prompt: A radioactive sample starts with 100.5 mg. Its half-life is 4 hours. How many mg remain after 9.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=100.5 mg, t=9.5 h, and T_half=4 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 = 5.03 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 503.4376, "unit": "g"}

Answer: 503.4376

Prompt: A sample contains 5.03 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 = 5.03 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 280 mL to 0.28 L.
3. Compute M = 3.095 / 0.28.
Final: {"answer": 11.0536, "unit": "mol/L"}

Answer: 11.0536

Prompt: A solution contains 3.095 mol of solute in 280 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 280 mL to 0.28 L.
Compute M = 3.095 / 0.28.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 33.5622, "unit": "state_units"}

Answer: 33.5622

Prompt: Use explicit Euler on dy/dt = -0.56 y with y(0)=40, step size h=0.15, 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) = -0.56 y, so each step multiplies y by 1 - h*0.56.
Apply that update for 2 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(2.5)=7.25 and f(7.4)=-0.1.
3. The interval width is 4.9.
Final: {"answer": 17.5175, "unit": "area_units"}

Answer: 17.5175

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+11 from x=2.5 to x=7.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.5)=7.25 and f(7.4)=-0.1.
The interval width is 4.9.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 192.5 + 273.15.
Final: {"answer": 465.65, "unit": "K"}

Answer: 465.65

Prompt: Convert 192.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 192.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=338 degrees and keep the unit as newtons.
Final: {"answer": [4.6359, -1.873], "unit": "N"}

Answer: 4.6359

Answer: -1.873

Prompt: A vector has magnitude 5 N at 338 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=338 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": [7.7, 16.0], "unit": "dimensionless"}

Answer: 7.7

Answer: 16.0

Prompt: A line passes through points (-18.75, -128.375) and (-14.5, -95.65). 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. 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 field worksheet case 324738, 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 normalize_007936(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_007936"}

Answer: python_code

Prompt: Write a Python function normalize_007936(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_007936([2, 3, 5]); assert len(out) == 3

try:
    normalize_007936([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: 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 field survey records in release 518908, 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. Use Newton's second law F = m a.
2. Substitute m = 16.95 kg and a = 11.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 199.1625, "unit": "N"}

Answer: 199.1625

Prompt: A cart has mass 16.95 kg and measured acceleration 11.75 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 = 16.95 kg and a = 11.75 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=79 degrees through the sine of 2 theta.
3. Substitute v=42.9 m/s and g=9.81 m/s^2.
Final: {"answer": 70.2783, "unit": "m"}

Answer: 70.2783

Prompt: A projectile is launched on level ground with no air resistance at speed 42.9 m/s and angle 79 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=79 degrees through the sine of 2 theta.
Substitute v=42.9 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 = 3.68 * 8.314 * 244 / 37.2.
Final: {"answer": 200.6803, "unit": "kPa"}

Answer: 200.6803

Prompt: An ideal gas sample has n=3.68 mol, T=244 K, and V=37.2 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 = 3.68 * 8.314 * 244 / 37.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 430 * 4.865 * 58.
Final: {"answer": 121333.1, "unit": "J"}

Answer: 121333.1

Prompt: A 430 g sample has specific heat 4.865 J/(g*K). How much heat is needed to raise its temperature by 58 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 430 * 4.865 * 58.


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=203.4 V and R=23.3 ohm.
Final: {"answer": 1775.6034, "unit": "W"}

Answer: 1775.6034

Prompt: A resistor has resistance 23.3 ohm and voltage 203.4 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=203.4 V and R=23.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=504.5 mg, t=143.5 h, and T_half=17.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.7156, "unit": "mg"}

Answer: 1.7156

Prompt: A radioactive sample starts with 504.5 mg. Its half-life is 17.5 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=504.5 mg, t=143.5 h, and T_half=17.5 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 = 7.66 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 137.9949, "unit": "g"}

Answer: 137.9949

Prompt: A sample contains 7.66 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 = 7.66 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 2870 mL to 2.87 L.
3. Compute M = 0.89 / 2.87.
Final: {"answer": 0.3101, "unit": "mol/L"}

Answer: 0.3101

Prompt: A solution contains 0.89 mol of solute in 2870 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2870 mL to 2.87 L.
Compute M = 0.89 / 2.87.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7)=31.9 and f(-2.7)=1.37.
3. The interval width is 4.3.
Final: {"answer": 71.5305, "unit": "area_units"}

Answer: 71.5305

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+-17.8 from x=-7 to x=-2.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7)=31.9 and f(-2.7)=1.37.
The interval width is 4.3.


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=0.42 and add it to the current value.
Final: {"answer": [0.516, 0.451, 1.157], "unit": "temperature_units"}

Answer: 0.516

Answer: 0.451

Answer: 1.157

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=-0.5, right=0.55; current interior values are [-0.45, 1.9, 0.8]. Use r=0.42. 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=0.42 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 37632.0 / 1000.
Final: {"answer": 37.632, "unit": "kg"}

Answer: 37.632

Prompt: Convert 37632 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 37632.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=167 degrees and keep the unit as newtons.
Final: {"answer": [-77.4624, 17.8836], "unit": "N"}

Answer: -77.4624

Answer: 17.8836

Prompt: A vector has magnitude 79.5 N at 167 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=167 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 791958, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
speed squared over acceleration has units of meters
The equation is valid only if both sides have identical dimensions.

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_007954(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_007954"}

Answer: python_code

Prompt: Write a Python function safe_mean_007954(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_007954([])
    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 alignment scoring problem with 3709 items and budget 2270, 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 = 17 kg and a = 8.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 149.6, "unit": "N"}

Answer: 149.6

Prompt: A cart has mass 17 kg and measured acceleration 8.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17 kg and a = 8.8 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 = 37.5^2 and multiply by 0.5 * 21.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 15152.3438, "unit": "J"}

Answer: 15152.3438

Prompt: A body of mass 21.55 kg moves at 37.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.5^2 and multiply by 0.5 * 21.55.
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 = 4.69 * 8.314 * 430 / 47.6.
Final: {"answer": 352.2446, "unit": "kPa"}

Answer: 352.2446

Prompt: An ideal gas sample has n=4.69 mol, T=430 K, and V=47.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.69 * 8.314 * 430 / 47.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 385 * 4.7 * 87.
Final: {"answer": 157426.5, "unit": "J"}

Answer: 157426.5

Prompt: A 385 g sample has specific heat 4.7 J/(g*K). How much heat is needed to raise its temperature by 87 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 385 * 4.7 * 87.


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=202.7 V and R=99.3 ohm.
Final: {"answer": 413.7693, "unit": "W"}

Answer: 413.7693

Prompt: A resistor has resistance 99.3 ohm and voltage 202.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=202.7 V and R=99.3 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.17 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 93.1376, "unit": "g"}

Answer: 93.1376

Prompt: A sample contains 5.17 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 = 5.17 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 4435 mL to 4.435 L.
3. Compute M = 0.695 / 4.435.
Final: {"answer": 0.1567, "unit": "mol/L"}

Answer: 0.1567

Prompt: A solution contains 0.695 mol of solute in 4435 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4435 mL to 4.435 L.
Compute M = 0.695 / 4.435.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.66 y, so each step multiplies y by 1 - h*0.66.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.001, "unit": "state_units"}

Answer: 0.001

Prompt: Use explicit Euler on dy/dt = -0.66 y with y(0)=49.5, step size h=0.9, 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) = -0.66 y, so each step multiplies y by 1 - h*0.66.
Apply that update for 12 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(-0.5)=15.4 and f(3.4)=39.58.
3. The interval width is 3.9.
Final: {"answer": 107.211, "unit": "area_units"}

Answer: 107.211

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.2x+18.5 from x=-0.5 to x=3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.5)=15.4 and f(3.4)=39.58.
The interval width is 3.9.


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=0.12 and add it to the current value.
Final: {"answer": [1.876, 1.632, -0.326], "unit": "temperature_units"}

Answer: 1.876

Answer: 1.632

Answer: -0.326

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.2, right=2.3; current interior values are [2.35, 1.95, -1.1]. Use r=0.12. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.12 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2135.5 / 100.
Final: {"answer": 21.355, "unit": "m"}

Answer: 21.355

Prompt: Convert 2135.5 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 2135.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=274 degrees and keep the unit as newtons.
Final: {"answer": [16.602, -237.4202], "unit": "N"}

Answer: 16.602

Answer: -237.4202

Prompt: A vector has magnitude 238 N at 274 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=274 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In lab notebook case 730427, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
mass times acceleration has newton dimensions
The equation is valid only if both sides have identical dimensions.

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_007972(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_007972"}

Answer: python_code

Prompt: Write a Python function normalize_007972(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_007972([2, 3, 5]); assert len(out) == 3

try:
    normalize_007972([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: 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 warehouse experiment records in release 16210, 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. Use Newton's second law F = m a.
2. Substitute m = 20.65 kg and a = 0.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 10.325, "unit": "N"}

Answer: 10.325

Prompt: A cart has mass 20.65 kg and measured acceleration 0.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.65 kg and a = 0.5 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 = 31.4^2 and multiply by 0.5 * 12.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6310.144, "unit": "J"}

Answer: 6310.144

Prompt: A body of mass 12.8 kg moves at 31.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.4^2 and multiply by 0.5 * 12.8.
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=56 degrees through the sine of 2 theta.
3. Substitute v=40.9 m/s and g=9.81 m/s^2.
Final: {"answer": 158.1042, "unit": "m"}

Answer: 158.1042

Prompt: A projectile is launched on level ground with no air resistance at speed 40.9 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=56 degrees through the sine of 2 theta.
Substitute v=40.9 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 = 3.48 * 8.314 * 332 / 89.2.
Final: {"answer": 107.6868, "unit": "kPa"}

Answer: 107.6868

Prompt: An ideal gas sample has n=3.48 mol, T=332 K, and V=89.2 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 = 3.48 * 8.314 * 332 / 89.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 650 * 4.49 * 59.
Final: {"answer": 172191.5, "unit": "J"}

Answer: 172191.5

Prompt: A 650 g sample has specific heat 4.49 J/(g*K). How much heat is needed to raise its temperature by 59 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 650 * 4.49 * 59.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=750 mg, t=292 h, and T_half=96 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 91.0811, "unit": "mg"}

Answer: 91.0811

Prompt: A radioactive sample starts with 750 mg. Its half-life is 96 hours. How many mg remain after 292 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=750 mg, t=292 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 = 0.59 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 34.4796, "unit": "g"}

Answer: 34.4796

Prompt: A sample contains 0.59 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.59 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 1285 mL to 1.285 L.
3. Compute M = 0.395 / 1.285.
Final: {"answer": 0.3074, "unit": "mol/L"}

Answer: 0.3074

Prompt: A solution contains 0.395 mol of solute in 1285 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1285 mL to 1.285 L.
Compute M = 0.395 / 1.285.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 18.2, "unit": "state_units"}

Answer: 18.2

Prompt: Use explicit Euler on dy/dt = -0.17 y with y(0)=56.5, step size h=1.85, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
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(0.9)=-8.03 and f(3.6)=-12.62.
3. The interval width is 2.7.
Final: {"answer": -27.8775, "unit": "area_units"}

Answer: -27.8775

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.7x+-6.5 from x=0.9 to x=3.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.9)=-8.03 and f(3.6)=-12.62.
The interval width is 2.7.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1591.0 / 100.
Final: {"answer": 15.91, "unit": "m"}

Answer: 15.91

Prompt: Convert 1591 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 1591.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=130 degrees and keep the unit as newtons.
Final: {"answer": [-129.8431, 154.741], "unit": "N"}

Answer: -129.8431

Answer: 154.741

Prompt: A vector has magnitude 202 N at 130 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=130 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In lab notebook case 665977, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
coulomb per second is ampere
The equation is valid only if both sides have identical dimensions.

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_007990(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_007990"}

Answer: python_code

Prompt: Write a Python function normalize_007990(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_007990([2, 3, 5]); assert len(out) == 3

try:
    normalize_007990([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 12.2^2 and multiply by 0.5 * 3.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 275.354, "unit": "J"}

Answer: 275.354

Prompt: A body of mass 3.7 kg moves at 12.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.2^2 and multiply by 0.5 * 3.7.
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=20 degrees through the sine of 2 theta.
3. Substitute v=18.4 m/s and g=9.81 m/s^2.
Final: {"answer": 22.1837, "unit": "m"}

Answer: 22.1837

Prompt: A projectile is launched on level ground with no air resistance at speed 18.4 m/s and angle 20 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=20 degrees through the sine of 2 theta.
Substitute v=18.4 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 = 3.11 * 8.314 * 301 / 32.0.
Final: {"answer": 243.2131, "unit": "kPa"}

Answer: 243.2131

Prompt: An ideal gas sample has n=3.11 mol, T=301 K, and V=32.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.11 * 8.314 * 301 / 32.0.


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=127.6 V and R=83.7 ohm.
Final: {"answer": 194.5252, "unit": "W"}

Answer: 194.5252

Prompt: A resistor has resistance 83.7 ohm and voltage 127.6 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=127.6 V and R=83.7 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 655 mL to 0.655 L.
3. Compute M = 3.54 / 0.655.
Final: {"answer": 5.4046, "unit": "mol/L"}

Answer: 5.4046

Prompt: A solution contains 3.54 mol of solute in 655 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 655 mL to 0.655 L.
Compute M = 3.54 / 0.655.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 18.0123, "unit": "state_units"}

Answer: 18.0123

Prompt: Use explicit Euler on dy/dt = -0.17 y with y(0)=58.5, step size h=0.55, 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) = -0.17 y, so each step multiplies y by 1 - h*0.17.
Apply that update for 12 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(1.3)=9.43 and f(10.1)=63.11.
3. The interval width is 8.8.
Final: {"answer": 319.176, "unit": "area_units"}

Answer: 319.176

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.1x+1.5 from x=1.3 to x=10.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.3)=9.43 and f(10.1)=63.11.
The interval width is 8.8.


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": [-0.16, -1.382, 1.126], "unit": "temperature_units"}

Answer: -0.16

Answer: -1.382

Answer: 1.126

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.2; current interior values are [-0.2, -1.55, 1.3]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22137.0 / 1000.
Final: {"answer": 22.137, "unit": "kg"}

Answer: 22.137

Prompt: Convert 22137 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 22137.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=164 degrees and keep the unit as newtons.
Final: {"answer": [-411.42, 117.9728], "unit": "N"}

Answer: -411.42

Answer: 117.9728

Prompt: A vector has magnitude 428 N at 164 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=164 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": [4.1, -6.25], "unit": "dimensionless"}

Answer: 4.1

Answer: -6.25

Prompt: A line passes through points (-19.25, -85.175) and (-16.75, -74.925). 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 student derivation case 174150, 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 safe_mean_008008(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_008008"}

Answer: python_code

Prompt: Write a Python function safe_mean_008008(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_008008([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 3.25^2 and multiply by 0.5 * 10.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 53.6047, "unit": "J"}

Answer: 53.6047

Prompt: A body of mass 10.15 kg moves at 3.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.25^2 and multiply by 0.5 * 10.15.
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=68 degrees through the sine of 2 theta.
3. Substitute v=81.1 m/s and g=9.81 m/s^2.
Final: {"answer": 465.7405, "unit": "m"}

Answer: 465.7405

Prompt: A projectile is launched on level ground with no air resistance at speed 81.1 m/s and angle 68 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=68 degrees through the sine of 2 theta.
Substitute v=81.1 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 = 0.39 * 8.314 * 442 / 72.6.
Final: {"answer": 19.7406, "unit": "kPa"}

Answer: 19.7406

Prompt: An ideal gas sample has n=0.39 mol, T=442 K, and V=72.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.39 * 8.314 * 442 / 72.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1195 * 1.42 * 16.
Final: {"answer": 27150.4, "unit": "J"}

Answer: 27150.4

Prompt: A 1195 g sample has specific heat 1.42 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1195 * 1.42 * 16.


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=62.5 V and R=129 ohm.
Final: {"answer": 30.281, "unit": "W"}

Answer: 30.281

Prompt: A resistor has resistance 129 ohm and voltage 62.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=62.5 V and R=129 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=858.5 mg, t=334 h, and T_half=42.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 3.6983, "unit": "mg"}

Answer: 3.6983

Prompt: A radioactive sample starts with 858.5 mg. Its half-life is 42.5 hours. How many mg remain after 334 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=858.5 mg, t=334 h, and T_half=42.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.8)=-1.72 and f(2.8)=3.48.
3. The interval width is 2.
Final: {"answer": 1.76, "unit": "area_units"}

Answer: 1.76

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.6x+-3.8 from x=0.8 to x=2.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.8)=-1.72 and f(2.8)=3.48.
The interval width is 2.


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=0.02 and add it to the current value.
Final: {"answer": [2.325, 2.054, 1.86], "unit": "temperature_units"}

Answer: 2.325

Answer: 2.054

Answer: 1.86

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=-0.25; current interior values are [2.4, 2.05, 1.9]. Use r=0.02. 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=0.02 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 12111.0 / 1000.
Final: {"answer": 12.111, "unit": "kg"}

Answer: 12.111

Prompt: Convert 12111 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 12111.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=7 degrees and keep the unit as newtons.
Final: {"answer": [446.1495, 54.7803], "unit": "N"}

Answer: 446.1495

Answer: 54.7803

Prompt: A vector has magnitude 449.5 N at 7 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=7 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": [9.4, 15.25], "unit": "dimensionless"}

Answer: 9.4

Answer: 15.25

Prompt: A line passes through points (-17, -144.55) and (-9, -69.35). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 25112, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
grams cancel with J/(g*K), and kelvin cancels, leaving joules
The equation is valid only if both sides have identical dimensions.

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_008026(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_008026"}

Answer: python_code

Prompt: Write a Python function safe_mean_008026(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_008026([])
    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 laboratory sensor record from batch 943161 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 = 10.65 kg and a = 14.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 153.36, "unit": "N"}

Answer: 153.36

Prompt: A cart has mass 10.65 kg and measured acceleration 14.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.65 kg and a = 14.4 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 = 27.2^2 and multiply by 0.5 * 22.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 8304.704, "unit": "J"}

Answer: 8304.704

Prompt: A body of mass 22.45 kg moves at 27.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 27.2^2 and multiply by 0.5 * 22.45.
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=57 degrees through the sine of 2 theta.
3. Substitute v=20.4 m/s and g=9.81 m/s^2.
Final: {"answer": 38.7544, "unit": "m"}

Answer: 38.7544

Prompt: A projectile is launched on level ground with no air resistance at speed 20.4 m/s and angle 57 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=57 degrees through the sine of 2 theta.
Substitute v=20.4 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 = 4.08 * 8.314 * 332 / 15.8.
Final: {"answer": 712.7729, "unit": "kPa"}

Answer: 712.7729

Prompt: An ideal gas sample has n=4.08 mol, T=332 K, and V=15.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.08 * 8.314 * 332 / 15.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1555 * 1.755 * 64.
Final: {"answer": 174657.6, "unit": "J"}

Answer: 174657.6

Prompt: A 1555 g sample has specific heat 1.755 J/(g*K). How much heat is needed to raise its temperature by 64 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1555 * 1.755 * 64.


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=142.1 V and R=40.1 ohm.
Final: {"answer": 503.5514, "unit": "W"}

Answer: 503.5514

Prompt: A resistor has resistance 40.1 ohm and voltage 142.1 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=142.1 V and R=40.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=45 mg, t=16 h, and T_half=92 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 39.8896, "unit": "mg"}

Answer: 39.8896

Prompt: A radioactive sample starts with 45 mg. Its half-life is 92 hours. How many mg remain after 16 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=45 mg, t=16 h, and T_half=92 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 = 3.61 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 650.3632, "unit": "g"}

Answer: 650.3632

Prompt: A sample contains 3.61 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 = 3.61 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 2155 mL to 2.155 L.
3. Compute M = 3.995 / 2.155.
Final: {"answer": 1.8538, "unit": "mol/L"}

Answer: 1.8538

Prompt: A solution contains 3.995 mol of solute in 2155 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2155 mL to 2.155 L.
Compute M = 3.995 / 2.155.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.76 y, so each step multiplies y by 1 - h*0.76.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": -1.0706, "unit": "state_units"}

Answer: -1.0706

Prompt: Use explicit Euler on dy/dt = -0.76 y with y(0)=43, step size h=1.7, 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) = -0.76 y, so each step multiplies y by 1 - h*0.76.
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(-4.3)=8.81 and f(0.9)=-20.83.
3. The interval width is 5.2.
Final: {"answer": -31.252, "unit": "area_units"}

Answer: -31.252

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.7x+-15.7 from x=-4.3 to x=0.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.3)=8.81 and f(0.9)=-20.83.
The interval width is 5.2.


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=0.18 and add it to the current value.
Final: {"answer": [1.497, 0.111, -0.401], "unit": "temperature_units"}

Answer: 1.497

Answer: 0.111

Answer: -0.401

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=1.3; current interior values are [2.1, -0.15, -0.95]. Use r=0.18. 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=0.18 and add it to the current value.