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": [-0.6, 7.5], "unit": "dimensionless"}

Answer: -0.6

Answer: 7.5

Prompt: A line passes through points (8, 2.7) and (8.25, 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. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In quality-control check case 243692, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
amount times volume is not concentration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def pairwise_ratios_006928(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_006928"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_006928(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

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

try:
    pairwise_ratios_006928([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_006928([1, 2], [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 registry invoice records in release 776427, 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 = 9.3 kg and a = 9.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 86.025, "unit": "N"}

Answer: 86.025

Prompt: A cart has mass 9.3 kg and measured acceleration 9.25 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 = 9.3 kg and a = 9.25 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 = 6.75^2 and multiply by 0.5 * 13.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 313.2422, "unit": "J"}

Answer: 313.2422

Prompt: A body of mass 13.75 kg moves at 6.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.75^2 and multiply by 0.5 * 13.75.
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=75 degrees through the sine of 2 theta.
3. Substitute v=82.9 m/s and g=9.81 m/s^2.
Final: {"answer": 350.2757, "unit": "m"}

Answer: 350.2757

Prompt: A projectile is launched on level ground with no air resistance at speed 82.9 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=75 degrees through the sine of 2 theta.
Substitute v=82.9 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 = 4.96 * 8.314 * 572 / 69.5.
Final: {"answer": 339.393, "unit": "kPa"}

Answer: 339.393

Prompt: An ideal gas sample has n=4.96 mol, T=572 K, and V=69.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.96 * 8.314 * 572 / 69.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1070 * 2.43 * 113.
Final: {"answer": 293811.3, "unit": "J"}

Answer: 293811.3

Prompt: A 1070 g sample has specific heat 2.43 J/(g*K). How much heat is needed to raise its temperature by 113 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1070 * 2.43 * 113.


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=66.4 V and R=187.3 ohm.
Final: {"answer": 23.5396, "unit": "W"}

Answer: 23.5396

Prompt: A resistor has resistance 187.3 ohm and voltage 66.4 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=66.4 V and R=187.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=814.5 mg, t=234.5 h, and T_half=38.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 11.9494, "unit": "mg"}

Answer: 11.9494

Prompt: A radioactive sample starts with 814.5 mg. Its half-life is 38.5 hours. How many mg remain after 234.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=814.5 mg, t=234.5 h, and T_half=38.5 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 = 5.61 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 561.4881, "unit": "g"}

Answer: 561.4881

Prompt: A sample contains 5.61 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 = 5.61 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 3780 mL to 3.78 L.
3. Compute M = 1.39 / 3.78.
Final: {"answer": 0.3677, "unit": "mol/L"}

Answer: 0.3677

Prompt: A solution contains 1.39 mol of solute in 3780 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3780 mL to 3.78 L.
Compute M = 1.39 / 3.78.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.3)=-11.76 and f(-1.1)=-10.52.
3. The interval width is 0.2.
Final: {"answer": -2.228, "unit": "area_units"}

Answer: -2.228

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.2x+-3.7 from x=-1.3 to x=-1.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.3)=-11.76 and f(-1.1)=-10.52.
The interval width is 0.2.

(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=0.34 and add it to the current value.
Final: {"answer": [-0.559, 0.608, 1.106], "unit": "temperature_units"}

Answer: -0.559

Answer: 0.608

Answer: 1.106

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.7, right=2.35; current interior values are [0.75, -0.65, 1.65]. Use r=0.34. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.34 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 414.0 / 100.
Final: {"answer": 4.14, "unit": "m"}

Answer: 4.14

Prompt: Convert 414 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 414.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=334 degrees and keep the unit as newtons.
Final: {"answer": [390.0766, -190.2531], "unit": "N"}

Answer: 390.0766

Answer: -190.2531

Prompt: A vector has magnitude 434 N at 334 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=334 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": [6.1, 20.5], "unit": "dimensionless"}

Answer: 6.1

Answer: 20.5

Prompt: A line passes through points (16.25, 119.625) and (22.25, 156.225). 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 lab notebook case 495385, 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 running_total_006946(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_006946"}

Answer: python_code

Prompt: Write a Python function running_total_006946(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: 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 field crop record from batch 322195 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 = 2.75 kg and a = 2.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 7.15, "unit": "N"}

Answer: 7.15

Prompt: A cart has mass 2.75 kg and measured acceleration 2.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.75 kg and a = 2.6 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 = 25.25^2 and multiply by 0.5 * 17.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5610.55, "unit": "J"}

Answer: 5610.55

Prompt: A body of mass 17.6 kg moves at 25.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.25^2 and multiply by 0.5 * 17.6.
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=57 degrees through the sine of 2 theta.
3. Substitute v=10.4 m/s and g=9.81 m/s^2.
Final: {"answer": 10.0723, "unit": "m"}

Answer: 10.0723

Prompt: A projectile is launched on level ground with no air resistance at speed 10.4 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=10.4 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 = 4.95 * 8.314 * 520 / 15.5.
Final: {"answer": 1380.6604, "unit": "kPa"}

Answer: 1380.6604

Prompt: An ideal gas sample has n=4.95 mol, T=520 K, and V=15.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.95 * 8.314 * 520 / 15.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1180 * 4.57 * 24.
Final: {"answer": 129422.4, "unit": "J"}

Answer: 129422.4

Prompt: A 1180 g sample has specific heat 4.57 J/(g*K). How much heat is needed to raise its temperature by 24 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1180 * 4.57 * 24.


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=193.6 V and R=119 ohm.
Final: {"answer": 314.9661, "unit": "W"}

Answer: 314.9661

Prompt: A resistor has resistance 119 ohm and voltage 193.6 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=193.6 V and R=119 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=319.5 mg, t=81.5 h, and T_half=10 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.1248, "unit": "mg"}

Answer: 1.1248

Prompt: A radioactive sample starts with 319.5 mg. Its half-life is 10 hours. How many mg remain after 81.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=319.5 mg, t=81.5 h, and T_half=10 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 26.2567, "unit": "state_units"}

Answer: 26.2567

Prompt: Use explicit Euler on dy/dt = -0.23 y with y(0)=27.5, step size h=0.05, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.8)=-0.88 and f(14.8)=3.12.
3. The interval width is 10.
Final: {"answer": 11.2, "unit": "area_units"}

Answer: 11.2

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.4x+-2.8 from x=4.8 to x=14.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.8)=-0.88 and f(14.8)=3.12.
The interval width is 10.


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=0.22 and add it to the current value.
Final: {"answer": [0.186, -0.061, 0.5], "unit": "temperature_units"}

Answer: 0.186

Answer: -0.061

Answer: 0.5

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=2.55, right=1.05; current interior values are [-0.65, -0.05, 0.5]. Use r=0.22. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.22 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 30940.0 / 1000.
Final: {"answer": 30.94, "unit": "kg"}

Answer: 30.94

Prompt: Convert 30940 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 30940.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=303 degrees and keep the unit as newtons.
Final: {"answer": [52.013, -80.093], "unit": "N"}

Answer: 52.013

Answer: -80.093

Prompt: A vector has magnitude 95.5 N at 303 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=303 degrees and keep the unit as newtons.


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 950253, 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 normalize_006964(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_006964"}

Answer: python_code

Prompt: Write a Python function normalize_006964(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_006964([2, 3, 5]); assert len(out) == 3

try:
    normalize_006964([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: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=3.5 mol and T=488 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 = 3.65 kg and a = 1.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 4.38, "unit": "N"}

Answer: 4.38

Prompt: A cart has mass 3.65 kg and measured acceleration 1.2 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 = 3.65 kg and a = 1.2 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 = 5.75^2 and multiply by 0.5 * 22.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 366.9937, "unit": "J"}

Answer: 366.9937

Prompt: A body of mass 22.2 kg moves at 5.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.75^2 and multiply by 0.5 * 22.2.
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=76 degrees through the sine of 2 theta.
3. Substitute v=43.8 m/s and g=9.81 m/s^2.
Final: {"answer": 91.8097, "unit": "m"}

Answer: 91.8097

Prompt: A projectile is launched on level ground with no air resistance at speed 43.8 m/s and angle 76 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=76 degrees through the sine of 2 theta.
Substitute v=43.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.67 * 8.314 * 525 / 23.4.
Final: {"answer": 311.5085, "unit": "kPa"}

Answer: 311.5085

Prompt: An ideal gas sample has n=1.67 mol, T=525 K, and V=23.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.67 * 8.314 * 525 / 23.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1110 * 2.24 * 80.
Final: {"answer": 198912.0, "unit": "J"}

Answer: 198912.0

Prompt: A 1110 g sample has specific heat 2.24 J/(g*K). How much heat is needed to raise its temperature by 80 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1110 * 2.24 * 80.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=13 V and R=2.5 ohm.
Final: {"answer": 67.6, "unit": "W"}

Answer: 67.6

Prompt: A resistor has resistance 2.5 ohm and voltage 13 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=13 V and R=2.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.63 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 137.4545, "unit": "g"}

Answer: 137.4545

Prompt: A sample contains 7.63 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 = 7.63 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 490 mL to 0.49 L.
3. Compute M = 1.63 / 0.49.
Final: {"answer": 3.3265, "unit": "mol/L"}

Answer: 3.3265

Prompt: A solution contains 1.63 mol of solute in 490 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 490 mL to 0.49 L.
Compute M = 1.63 / 0.49.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.7)=-3.15 and f(10.2)=10.6.
3. The interval width is 5.5.
Final: {"answer": 20.4875, "unit": "area_units"}

Answer: 20.4875

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.5x+-14.9 from x=4.7 to x=10.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.7)=-3.15 and f(10.2)=10.6.
The interval width is 5.5.


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=0.24 and add it to the current value.
Final: {"answer": [-0.626, -1.082, -0.212], "unit": "temperature_units"}

Answer: -0.626

Answer: -1.082

Answer: -0.212

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=0.45; current interior values are [-1.25, -1.55, 0.1]. Use r=0.24. 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=0.24 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 2035.0 / 100.
Final: {"answer": 20.35, "unit": "m"}

Answer: 20.35

Prompt: Convert 2035 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 2035.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=213 degrees and keep the unit as newtons.
Final: {"answer": [-206.7323, -134.2535], "unit": "N"}

Answer: -206.7323

Answer: -134.2535

Prompt: A vector has magnitude 246.5 N at 213 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=213 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.4, 27.25], "unit": "dimensionless"}

Answer: 1.4

Answer: 27.25

Prompt: A line passes through points (2, 30.05) and (15.25, 48.6). 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. energy divided by length is force, not spring constant
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In model card equation case 836348, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
energy divided by length is force, not spring constant
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
import math

def unit_vector_006982(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_006982"}

Answer: python_code

Prompt: Write a Python function unit_vector_006982(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_006982(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 19.4 kg and a = 1.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 21.34, "unit": "N"}

Answer: 21.34

Prompt: A cart has mass 19.4 kg and measured acceleration 1.1 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 = 19.4 kg and a = 1.1 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 = 25.55^2 and multiply by 0.5 * 6.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2219.5285, "unit": "J"}

Answer: 2219.5285

Prompt: A body of mass 6.8 kg moves at 25.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.55^2 and multiply by 0.5 * 6.8.
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=81 degrees through the sine of 2 theta.
3. Substitute v=70.2 m/s and g=9.81 m/s^2.
Final: {"answer": 155.2343, "unit": "m"}

Answer: 155.2343

Prompt: A projectile is launched on level ground with no air resistance at speed 70.2 m/s and angle 81 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=81 degrees through the sine of 2 theta.
Substitute v=70.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.06 * 8.314 * 599 / 60.4.
Final: {"answer": 252.3024, "unit": "kPa"}

Answer: 252.3024

Prompt: An ideal gas sample has n=3.06 mol, T=599 K, and V=60.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.06 * 8.314 * 599 / 60.4.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=440 mg, t=20 h, and T_half=77 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 367.5048, "unit": "mg"}

Answer: 367.5048

Prompt: A radioactive sample starts with 440 mg. Its half-life is 77 hours. How many mg remain after 20 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=440 mg, t=20 h, and T_half=77 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.52 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 66.8952, "unit": "g"}

Answer: 66.8952

Prompt: A sample contains 1.52 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 = 1.52 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 3845 mL to 3.845 L.
3. Compute M = 3.975 / 3.845.
Final: {"answer": 1.0338, "unit": "mol/L"}

Answer: 1.0338

Prompt: A solution contains 3.975 mol of solute in 3845 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3845 mL to 3.845 L.
Compute M = 3.975 / 3.845.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2)=-15.4 and f(6.2)=-34.26.
3. The interval width is 8.2.
Final: {"answer": -203.606, "unit": "area_units"}

Answer: -203.606

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.3x+-20 from x=-2 to x=6.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2)=-15.4 and f(6.2)=-34.26.
The interval width is 8.2.


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=0.4 and add it to the current value.
Final: {"answer": [1.87, 2.25, 0.6], "unit": "temperature_units"}

Answer: 1.87

Answer: 2.25

Answer: 0.6

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=2.35, right=-0.65; current interior values are [2.75, 0.95, 2.4]. Use r=0.4. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.4 and add it to the current value.


Response:
Reasoning:
1. The 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_007000(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_007000"}

Answer: python_code

Prompt: Write a Python function unit_vector_007000(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_007000(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: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.04 and interior values [2.75, -1.55, 1.15], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.1 kg and a = 6.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 87.42, "unit": "N"}

Answer: 87.42

Prompt: A cart has mass 14.1 kg and measured acceleration 6.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.1 kg and a = 6.2 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 = 12.5^2 and multiply by 0.5 * 0.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 27.3438, "unit": "J"}

Answer: 27.3438

Prompt: A body of mass 0.35 kg moves at 12.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.5^2 and multiply by 0.5 * 0.35.
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 = 1.51 * 8.314 * 313 / 90.0.
Final: {"answer": 43.6605, "unit": "kPa"}

Answer: 43.6605

Prompt: An ideal gas sample has n=1.51 mol, T=313 K, and V=90.0 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 = 1.51 * 8.314 * 313 / 90.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 985 * 1.89 * 31.
Final: {"answer": 57711.15, "unit": "J"}

Answer: 57711.15

Prompt: A 985 g sample has specific heat 1.89 J/(g*K). How much heat is needed to raise its temperature by 31 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 985 * 1.89 * 31.


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=84.7 V and R=140.7 ohm.
Final: {"answer": 50.9886, "unit": "W"}

Answer: 50.9886

Prompt: A resistor has resistance 140.7 ohm and voltage 84.7 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=84.7 V and R=140.7 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1315 mL to 1.315 L.
3. Compute M = 3.86 / 1.315.
Final: {"answer": 2.9354, "unit": "mol/L"}

Answer: 2.9354

Prompt: A solution contains 3.86 mol of solute in 1315 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1315 mL to 1.315 L.
Compute M = 3.86 / 1.315.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 2.1237, "unit": "state_units"}

Answer: 2.1237

Prompt: Use explicit Euler on dy/dt = -0.47 y with y(0)=57, step size h=0.55, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.5)=-51.3 and f(-6.1)=-48.9.
3. The interval width is 0.4.
Final: {"answer": -20.04, "unit": "area_units"}

Answer: -20.04

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6x+-12.3 from x=-6.5 to x=-6.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.5)=-51.3 and f(-6.1)=-48.9.
The interval width is 0.4.


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=0.46 and add it to the current value.
Final: {"answer": [0.898, 0.186, 0.497], "unit": "temperature_units"}

Answer: 0.898

Answer: 0.186

Answer: 0.497

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=-1.95; current interior values are [-0.85, 2.9, 0.75]. Use r=0.46. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.46 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3081.5 / 100.
Final: {"answer": 30.815, "unit": "m"}

Answer: 30.815

Prompt: Convert 3081.5 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 3081.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=109 degrees and keep the unit as newtons.
Final: {"answer": [-124.367, 361.1881], "unit": "N"}

Answer: -124.367

Answer: 361.1881

Prompt: A vector has magnitude 382 N at 109 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=109 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": [-4.3, -6.75], "unit": "dimensionless"}

Answer: -4.3

Answer: -6.75

Prompt: A line passes through points (4, -23.95) and (11.75, -57.275). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 386789, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def clamp_007018(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_007018"}

Answer: python_code

Prompt: Write a Python function clamp_007018(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_007018(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.45 kg and a = 1.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 14.5275, "unit": "N"}

Answer: 14.5275

Prompt: A cart has mass 7.45 kg and measured acceleration 1.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.45 kg and a = 1.95 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 = 16.05^2 and multiply by 0.5 * 20.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2672.6259, "unit": "J"}

Answer: 2672.6259

Prompt: A body of mass 20.75 kg moves at 16.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.05^2 and multiply by 0.5 * 20.75.
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=70 degrees through the sine of 2 theta.
3. Substitute v=72.4 m/s and g=9.81 m/s^2.
Final: {"answer": 343.4596, "unit": "m"}

Answer: 343.4596

Prompt: A projectile is launched on level ground with no air resistance at speed 72.4 m/s and angle 70 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=70 degrees through the sine of 2 theta.
Substitute v=72.4 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 = 3.15 * 8.314 * 306 / 15.6.
Final: {"answer": 513.7093, "unit": "kPa"}

Answer: 513.7093

Prompt: An ideal gas sample has n=3.15 mol, T=306 K, and V=15.6 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 = 3.15 * 8.314 * 306 / 15.6.


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=114.4 V and R=7.7 ohm.
Final: {"answer": 1699.6571, "unit": "W"}

Answer: 1699.6571

Prompt: A resistor has resistance 7.7 ohm and voltage 114.4 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=114.4 V and R=7.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=877 mg, t=287.5 h, and T_half=46 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 11.5229, "unit": "mg"}

Answer: 11.5229

Prompt: A radioactive sample starts with 877 mg. Its half-life is 46 hours. How many mg remain after 287.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=877 mg, t=287.5 h, and T_half=46 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.66 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 166.1444, "unit": "g"}

Answer: 166.1444

Prompt: A sample contains 1.66 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 = 1.66 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 2585 mL to 2.585 L.
3. Compute M = 3.905 / 2.585.
Final: {"answer": 1.5106, "unit": "mol/L"}

Answer: 1.5106

Prompt: A solution contains 3.905 mol of solute in 2585 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2585 mL to 2.585 L.
Compute M = 3.905 / 2.585.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.75 y, so each step multiplies y by 1 - h*0.75.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 0.0051, "unit": "state_units"}

Answer: 0.0051

Prompt: Use explicit Euler on dy/dt = -0.75 y with y(0)=32.5, step size h=1.35, 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) = -0.75 y, so each step multiplies y by 1 - h*0.75.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [0.19, 1.27, 1.47], "unit": "temperature_units"}

Answer: 0.19

Answer: 1.27

Answer: 1.47

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=-1.9, right=1.4; current interior values are [1.25, 1.75, 1.05]. 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 1600.0 / 100.
Final: {"answer": 16.0, "unit": "m"}

Answer: 16.0

Prompt: Convert 1600 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 1600.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=318 degrees and keep the unit as newtons.
Final: {"answer": [75.8008, -68.2513], "unit": "N"}

Answer: 75.8008

Answer: -68.2513

Prompt: A vector has magnitude 102 N at 318 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=318 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 sensor calibration case 416198, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def clamp_007036(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_007036"}

Answer: python_code

Prompt: Write a Python function clamp_007036(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_007036(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 58.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 12.1 kg and a = 12.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 151.25, "unit": "N"}

Answer: 151.25

Prompt: A cart has mass 12.1 kg and measured acceleration 12.5 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 = 12.1 kg and a = 12.5 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 = 21.05^2 and multiply by 0.5 * 11.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2492.4516, "unit": "J"}

Answer: 2492.4516

Prompt: A body of mass 11.25 kg moves at 21.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.05^2 and multiply by 0.5 * 11.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=28 degrees through the sine of 2 theta.
3. Substitute v=9.6 m/s and g=9.81 m/s^2.
Final: {"answer": 7.7884, "unit": "m"}

Answer: 7.7884

Prompt: A projectile is launched on level ground with no air resistance at speed 9.6 m/s and angle 28 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=28 degrees through the sine of 2 theta.
Substitute v=9.6 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 = 0.32 * 8.314 * 403 / 16.4.
Final: {"answer": 65.3764, "unit": "kPa"}

Answer: 65.3764

Prompt: An ideal gas sample has n=0.32 mol, T=403 K, and V=16.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.32 * 8.314 * 403 / 16.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 85 * 3.875 * 27.
Final: {"answer": 8893.125, "unit": "J"}

Answer: 8893.125

Prompt: A 85 g sample has specific heat 3.875 J/(g*K). How much heat is needed to raise its temperature by 27 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 85 * 3.875 * 27.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=632 mg, t=55.5 h, and T_half=33.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 200.4452, "unit": "mg"}

Answer: 200.4452

Prompt: A radioactive sample starts with 632 mg. Its half-life is 33.5 hours. How many mg remain after 55.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=632 mg, t=55.5 h, and T_half=33.5 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 2405 mL to 2.405 L.
3. Compute M = 0.17 / 2.405.
Final: {"answer": 0.0707, "unit": "mol/L"}

Answer: 0.0707

Prompt: A solution contains 0.17 mol of solute in 2405 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2405 mL to 2.405 L.
Compute M = 0.17 / 2.405.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.96 y with y(0)=3.5, step size h=0.95, 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) = -0.96 y, so each step multiplies y by 1 - h*0.96.
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(2.9)=-25.36 and f(8.6)=-67.54.
3. The interval width is 5.7.
Final: {"answer": -264.765, "unit": "area_units"}

Answer: -264.765

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+-3.9 from x=2.9 to x=8.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.9)=-25.36 and f(8.6)=-67.54.
The interval width is 5.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.24 and add it to the current value.
Final: {"answer": [-0.062, 0.102, 0.254], "unit": "temperature_units"}

Answer: -0.062

Answer: 0.102

Answer: 0.254

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=0.85; current interior values are [-0.95, 0.75, -0.25]. Use r=0.24. 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=0.24 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 9469.0 / 1000.
Final: {"answer": 9.469, "unit": "kg"}

Answer: 9.469

Prompt: Convert 9469 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 9469.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=82 degrees and keep the unit as newtons.
Final: {"answer": [43.5612, 309.9539], "unit": "N"}

Answer: 43.5612

Answer: 309.9539

Prompt: A vector has magnitude 313 N at 82 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=82 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": [-4.0, 23.0], "unit": "dimensionless"}

Answer: -4.0

Answer: 23.0

Prompt: A line passes through points (-6.5, 49) and (4.5, 5). 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 instrument manual case 37207, 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
import math

def unit_vector_007054(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_007054"}

Answer: python_code

Prompt: Write a Python function unit_vector_007054(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_007054(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: 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 scheduler scoring problem with 4822 items and budget 69820, 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=64 degrees through the sine of 2 theta.
3. Substitute v=56.8 m/s and g=9.81 m/s^2.
Final: {"answer": 259.1551, "unit": "m"}

Answer: 259.1551

Prompt: A projectile is launched on level ground with no air resistance at speed 56.8 m/s and angle 64 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=64 degrees through the sine of 2 theta.
Substitute v=56.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.87 * 8.314 * 519 / 70.8.
Final: {"answer": 235.8604, "unit": "kPa"}

Answer: 235.8604

Prompt: An ideal gas sample has n=3.87 mol, T=519 K, and V=70.8 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 = 3.87 * 8.314 * 519 / 70.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1640 * 4.32 * 120.
Final: {"answer": 850176.0, "unit": "J"}

Answer: 850176.0

Prompt: A 1640 g sample has specific heat 4.32 J/(g*K). How much heat is needed to raise its temperature by 120 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1640 * 4.32 * 120.


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=234 V and R=35.1 ohm.
Final: {"answer": 1560.0, "unit": "W"}

Answer: 1560.0

Prompt: A resistor has resistance 35.1 ohm and voltage 234 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=234 V and R=35.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=844.5 mg, t=139 h, and T_half=92 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 296.3348, "unit": "mg"}

Answer: 296.3348

Prompt: A radioactive sample starts with 844.5 mg. Its half-life is 92 hours. How many mg remain after 139 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=844.5 mg, t=139 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 = 4.19 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 419.3645, "unit": "g"}

Answer: 419.3645

Prompt: A sample contains 4.19 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 = 4.19 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 2035 mL to 2.035 L.
3. Compute M = 2.435 / 2.035.
Final: {"answer": 1.1966, "unit": "mol/L"}

Answer: 1.1966

Prompt: A solution contains 2.435 mol of solute in 2035 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2035 mL to 2.035 L.
Compute M = 2.435 / 2.035.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 2.7386, "unit": "state_units"}

Answer: 2.7386

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=21.5, step size h=0.3, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.7)=1.53 and f(3.4)=-33.66.
3. The interval width is 5.1.
Final: {"answer": -81.9315, "unit": "area_units"}

Answer: -81.9315

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.9x+-10.2 from x=-1.7 to x=3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.7)=1.53 and f(3.4)=-33.66.
The interval width is 5.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [0.634, 1.284, 2.532], "unit": "temperature_units"}

Answer: 0.634

Answer: 1.284

Answer: 2.532

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.1, right=1.05; current interior values are [0.65, 1.2, 2.8]. Use r=0.08. 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=0.08 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 7326.0 / 1000.
Final: {"answer": 7.326, "unit": "kg"}

Answer: 7.326

Prompt: Convert 7326 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 7326.0 / 1000.


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": [-8.8, 29.75], "unit": "dimensionless"}

Answer: -8.8

Answer: 29.75

Prompt: A line passes through points (19, -137.45) and (19.5, -141.85). 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
def normalize_007072(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_007072"}

Answer: python_code

Prompt: Write a Python function normalize_007072(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_007072([2, 3, 5]); assert len(out) == 3

try:
    normalize_007072([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 62.2 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.7 kg and a = 4.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 76.145, "unit": "N"}

Answer: 76.145

Prompt: A cart has mass 15.7 kg and measured acceleration 4.85 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 = 15.7 kg and a = 4.85 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 = 44.45^2 and multiply by 0.5 * 14.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 14028.1978, "unit": "J"}

Answer: 14028.1978

Prompt: A body of mass 14.2 kg moves at 44.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.45^2 and multiply by 0.5 * 14.2.
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=74 degrees through the sine of 2 theta.
3. Substitute v=34.8 m/s and g=9.81 m/s^2.
Final: {"answer": 65.4183, "unit": "m"}

Answer: 65.4183

Prompt: A projectile is launched on level ground with no air resistance at speed 34.8 m/s and angle 74 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=74 degrees through the sine of 2 theta.
Substitute v=34.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=83.5 V and R=13.3 ohm.
Final: {"answer": 524.2293, "unit": "W"}

Answer: 524.2293

Prompt: A resistor has resistance 13.3 ohm and voltage 83.5 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=83.5 V and R=13.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=33.5 mg, t=150.5 h, and T_half=106 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 12.521, "unit": "mg"}

Answer: 12.521

Prompt: A radioactive sample starts with 33.5 mg. Its half-life is 106 hours. How many mg remain after 150.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=33.5 mg, t=150.5 h, and T_half=106 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 = 3.78 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 680.9897, "unit": "g"}

Answer: 680.9897

Prompt: A sample contains 3.78 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 = 3.78 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 2680 mL to 2.68 L.
3. Compute M = 0.29 / 2.68.
Final: {"answer": 0.1082, "unit": "mol/L"}

Answer: 0.1082

Prompt: A solution contains 0.29 mol of solute in 2680 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2680 mL to 2.68 L.
Compute M = 0.29 / 2.68.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0002, "unit": "state_units"}

Answer: 0.0002

Prompt: Use explicit Euler on dy/dt = -0.99 y with y(0)=58, step size h=0.65, 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) = -0.99 y, so each step multiplies y by 1 - h*0.99.
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(-4.9)=-14.85 and f(1.8)=15.3.
3. The interval width is 6.7.
Final: {"answer": 1.5075, "unit": "area_units"}

Answer: 1.5075

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.5x+7.2 from x=-4.9 to x=1.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.9)=-14.85 and f(1.8)=15.3.
The interval width is 6.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.16 and add it to the current value.
Final: {"answer": [-0.452, -0.084, -0.734], "unit": "temperature_units"}

Answer: -0.452

Answer: -0.084

Answer: -0.734

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=1.5; current interior values are [-1.1, 0.5, -1.55]. Use r=0.16. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.16 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3493.0 / 100.
Final: {"answer": 34.93, "unit": "m"}

Answer: 34.93

Prompt: Convert 3493 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 3493.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=303 degrees and keep the unit as newtons.
Final: {"answer": [162.0301, -249.5045], "unit": "N"}

Answer: 162.0301

Answer: -249.5045

Prompt: A vector has magnitude 297.5 N at 303 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=303 degrees and keep the unit as newtons.


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_007090(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_007090"}

Answer: python_code

Prompt: Write a Python function safe_mean_007090(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_007090([])
    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 2938 items and budget 5965, 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 = 23.65 kg and a = 6.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 146.63, "unit": "N"}

Answer: 146.63

Prompt: A cart has mass 23.65 kg and measured acceleration 6.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.65 kg and a = 6.2 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 = 9.45^2 and multiply by 0.5 * 20.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 935.4437, "unit": "J"}

Answer: 935.4437

Prompt: A body of mass 20.95 kg moves at 9.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.45^2 and multiply by 0.5 * 20.95.
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=71 degrees through the sine of 2 theta.
3. Substitute v=62.7 m/s and g=9.81 m/s^2.
Final: {"answer": 246.7221, "unit": "m"}

Answer: 246.7221

Prompt: A projectile is launched on level ground with no air resistance at speed 62.7 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=62.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 830 * 1.525 * 19.
Final: {"answer": 24049.25, "unit": "J"}

Answer: 24049.25

Prompt: A 830 g sample has specific heat 1.525 J/(g*K). How much heat is needed to raise its temperature by 19 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 830 * 1.525 * 19.


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=50 V and R=155.1 ohm.
Final: {"answer": 16.1186, "unit": "W"}

Answer: 16.1186

Prompt: A resistor has resistance 155.1 ohm and voltage 50 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=50 V and R=155.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=894.5 mg, t=351 h, and T_half=54 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 9.8829, "unit": "mg"}

Answer: 9.8829

Prompt: A radioactive sample starts with 894.5 mg. Its half-life is 54 hours. How many mg remain after 351 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=894.5 mg, t=351 h, and T_half=54 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.54 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 654.569, "unit": "g"}

Answer: 654.569

Prompt: A sample contains 6.54 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.54 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 2440 mL to 2.44 L.
3. Compute M = 3.75 / 2.44.
Final: {"answer": 1.5369, "unit": "mol/L"}

Answer: 1.5369

Prompt: A solution contains 3.75 mol of solute in 2440 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2440 mL to 2.44 L.
Compute M = 3.75 / 2.44.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.4)=-68.72 and f(11.8)=-87.44.
3. The interval width is 2.4.
Final: {"answer": -187.392, "unit": "area_units"}

Answer: -187.392

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.8x+4.6 from x=9.4 to x=11.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.4)=-68.72 and f(11.8)=-87.44.
The interval width is 2.4.


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": [-0.07, -0.77, 0.02], "unit": "temperature_units"}

Answer: -0.07

Answer: -0.77

Answer: 0.02

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=1.2; current interior values are [-1.35, -1.15, 0.0]. Use r=0.4. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.4 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 29101.0 / 1000.
Final: {"answer": 29.101, "unit": "kg"}

Answer: 29.101

Prompt: Convert 29101 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 29101.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=34 degrees and keep the unit as newtons.
Final: {"answer": [257.0016, 173.3498], "unit": "N"}

Answer: 257.0016

Answer: 173.3498

Prompt: A vector has magnitude 310 N at 34 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=34 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": [-8.4, 21.25], "unit": "dimensionless"}

Answer: -8.4

Answer: 21.25

Prompt: A line passes through points (-12.25, 124.15) and (-9.25, 98.95). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 299588, 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: 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 clinical records in release 64048, 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 = 24.5 kg and a = 11.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 284.2, "unit": "N"}

Answer: 284.2

Prompt: A cart has mass 24.5 kg and measured acceleration 11.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.5 kg and a = 11.6 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 = 35.2^2 and multiply by 0.5 * 21.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13598.464, "unit": "J"}

Answer: 13598.464

Prompt: A body of mass 21.95 kg moves at 35.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 35.2^2 and multiply by 0.5 * 21.95.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.32 * 8.314 * 369 / 5.8.
Final: {"answer": 1756.0888, "unit": "kPa"}

Answer: 1756.0888

Prompt: An ideal gas sample has n=3.32 mol, T=369 K, and V=5.8 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 = 3.32 * 8.314 * 369 / 5.8.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.38 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 24.8607, "unit": "g"}

Answer: 24.8607

Prompt: A sample contains 1.38 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.38 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 835 mL to 0.835 L.
3. Compute M = 0.12 / 0.835.
Final: {"answer": 0.1437, "unit": "mol/L"}

Answer: 0.1437

Prompt: A solution contains 0.12 mol of solute in 835 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 835 mL to 0.835 L.
Compute M = 0.12 / 0.835.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 61.6289, "unit": "state_units"}

Answer: 61.6289

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=65.5, step size h=1, 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) = -0.03 y, so each step multiplies y by 1 - h*0.03.
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(-4.3)=12.48 and f(-0.5)=14.
3. The interval width is 3.8.
Final: {"answer": 50.312, "unit": "area_units"}

Answer: 50.312

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.4x+14.2 from x=-4.3 to x=-0.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.3)=12.48 and f(-0.5)=14.
The interval width is 3.8.


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=0.28 and add it to the current value.
Final: {"answer": [0.36, 0.65, 0.768], "unit": "temperature_units"}

Answer: 0.36

Answer: 0.65

Answer: 0.768

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.5; current interior values are [2.25, -1.45, 2.35]. Use r=0.28. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.28 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 247.5 + 273.15.
Final: {"answer": 520.65, "unit": "K"}

Answer: 520.65

Prompt: Convert 247.5 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 247.5 + 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=307 degrees and keep the unit as newtons.
Final: {"answer": [96.8922, -128.5803], "unit": "N"}

Answer: 96.8922

Answer: -128.5803

Prompt: A vector has magnitude 161 N at 307 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=307 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.9, 17.25], "unit": "dimensionless"}

Answer: 5.9

Answer: 17.25

Prompt: A line passes through points (-12.5, -56.5) and (-2.25, 3.975). 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 sensor calibration case 262402, 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 center_values_007126(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_007126"}

Answer: python_code

Prompt: Write a Python function center_values_007126(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_007126([])
    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 mobile ledger record from batch 109517 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 = 7.95 kg and a = 1.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 11.5275, "unit": "N"}

Answer: 11.5275

Prompt: A cart has mass 7.95 kg and measured acceleration 1.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.95 kg and a = 1.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 7.1^2 and multiply by 0.5 * 1.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 46.6292, "unit": "J"}

Answer: 46.6292

Prompt: A body of mass 1.85 kg moves at 7.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.1^2 and multiply by 0.5 * 1.85.
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=76 degrees through the sine of 2 theta.
3. Substitute v=56.6 m/s and g=9.81 m/s^2.
Final: {"answer": 153.3109, "unit": "m"}

Answer: 153.3109

Prompt: A projectile is launched on level ground with no air resistance at speed 56.6 m/s and angle 76 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=76 degrees through the sine of 2 theta.
Substitute v=56.6 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 = 1.29 * 8.314 * 324 / 8.4.
Final: {"answer": 413.6809, "unit": "kPa"}

Answer: 413.6809

Prompt: An ideal gas sample has n=1.29 mol, T=324 K, and V=8.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.29 * 8.314 * 324 / 8.4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=77.9 V and R=1.5 ohm.
Final: {"answer": 4045.6067, "unit": "W"}

Answer: 4045.6067

Prompt: A resistor has resistance 1.5 ohm and voltage 77.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=77.9 V and R=1.5 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1550 mL to 1.55 L.
3. Compute M = 2.365 / 1.55.
Final: {"answer": 1.5258, "unit": "mol/L"}

Answer: 1.5258

Prompt: A solution contains 2.365 mol of solute in 1550 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1550 mL to 1.55 L.
Compute M = 2.365 / 1.55.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 1.4948, "unit": "state_units"}

Answer: 1.4948

Prompt: Use explicit Euler on dy/dt = -0.05 y with y(0)=2, 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) = -0.05 y, so each step multiplies y by 1 - h*0.05.
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(-9.9)=36.11 and f(-1.7)=-4.07.
3. The interval width is 8.2.
Final: {"answer": 131.364, "unit": "area_units"}

Answer: 131.364

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-12.4 from x=-9.9 to x=-1.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.9)=36.11 and f(-1.7)=-4.07.
The interval width is 8.2.


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=0.12 and add it to the current value.
Final: {"answer": [-0.364, -1.614, -0.994], "unit": "temperature_units"}

Answer: -0.364

Answer: -1.614

Answer: -0.994

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.4, right=0.95; current interior values are [0.05, -1.95, -1.15]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 196.5 + 273.15.
Final: {"answer": 469.65, "unit": "K"}

Answer: 469.65

Prompt: Convert 196.5 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 196.5 + 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=349 degrees and keep the unit as newtons.
Final: {"answer": [475.1076, -92.3516], "unit": "N"}

Answer: 475.1076

Answer: -92.3516

Prompt: A vector has magnitude 484 N at 349 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=349 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": [6.5, 2.0], "unit": "dimensionless"}

Answer: 6.5

Answer: 2.0

Prompt: A line passes through points (0.5, 5.25) and (8.5, 57.25). 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.