Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=715.5 mg, t=104 h, and T_half=86 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 309.4378, "unit": "mg"}

Answer: 309.4378

Prompt: A radioactive sample starts with 715.5 mg. Its half-life is 86 hours. How many mg remain after 104 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=715.5 mg, t=104 h, and T_half=86 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4.4)=8.18 and f(1.4)=9.92.
3. The interval width is 5.8.
Final: {"answer": 52.49, "unit": "area_units"}

Answer: 52.49

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.3x+9.5 from x=-4.4 to x=1.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.4)=8.18 and f(1.4)=9.92.
The interval width is 5.8.

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


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0115, "unit": "state_units"}

Answer: 0.0115

Prompt: Use explicit Euler on dy/dt = -0.83 y with y(0)=8, step size h=0.8, 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) = -0.83 y, so each step multiplies y by 1 - h*0.83.
Apply that update for 6 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=0.38 and add it to the current value.
Final: {"answer": [-0.71, -0.547, -0.266], "unit": "temperature_units"}

Answer: -0.71

Answer: -0.547

Answer: -0.266

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=-1.35; current interior values are [-1.85, 0.65, 0.0]. Use r=0.38. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.38 and add it to the current value.


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

Answer: consistent

Prompt: In simulation spec case 27978, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_001672(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_001672"}

Answer: python_code

Prompt: Write a Python function unit_vector_001672(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_001672(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: 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 63.1 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 = 4.2 kg and a = 5.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 22.47, "unit": "N"}

Answer: 22.47

Prompt: A cart has mass 4.2 kg and measured acceleration 5.35 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 = 4.2 kg and a = 5.35 m/s^2.
The unit kg*m/s^2 is one newton.


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

```python
def weighted_sum_001690(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_001690"}

Answer: python_code

Prompt: Write a Python function weighted_sum_001690(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_001690([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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 = 3.72 * 8.314 * 443 / 28.9.
Final: {"answer": 474.0879, "unit": "kPa"}

Answer: 474.0879

Prompt: An ideal gas sample has n=3.72 mol, T=443 K, and V=28.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.72 * 8.314 * 443 / 28.9.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3795 mL to 3.795 L.
3. Compute M = 0.72 / 3.795.
Final: {"answer": 0.1897, "unit": "mol/L"}

Answer: 0.1897

Prompt: A solution contains 0.72 mol of solute in 3795 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3795 mL to 3.795 L.
Compute M = 0.72 / 3.795.


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": [-1.3, 23.0], "unit": "dimensionless"}

Answer: -1.3

Answer: 23.0

Prompt: A line passes through points (8, 12.6) and (20.25, -3.325). 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 x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=32 degrees and keep the unit as newtons.
Final: {"answer": [76.7484, 47.9577], "unit": "N"}

Answer: 76.7484

Answer: 47.9577

Prompt: A vector has magnitude 90.5 N at 32 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=32 degrees and keep the unit as newtons.

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


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=182.8 V and R=18.1 ohm.
Final: {"answer": 1846.179, "unit": "W"}

Answer: 1846.179

Prompt: A resistor has resistance 18.1 ohm and voltage 182.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=182.8 V and R=18.1 ohm.


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_001762(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_001762"}

Answer: python_code

Prompt: Write a Python function safe_mean_001762(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_001762([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=92 degrees and keep the unit as newtons.
Final: {"answer": [-14.3437, 410.7496], "unit": "N"}

Answer: -14.3437

Answer: 410.7496

Prompt: A vector has magnitude 411 N at 92 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=92 degrees and keep the unit as newtons.


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 instrument manual case 883651, 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. 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 40 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 Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 595 * 0.73 * 18.
Final: {"answer": 7818.3, "unit": "J"}

Answer: 7818.3

Prompt: A 595 g sample has specific heat 0.73 J/(g*K). How much heat is needed to raise its temperature by 18 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 595 * 0.73 * 18.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4.5)=31.75 and f(-3.2)=27.2.
3. The interval width is 1.3.
Final: {"answer": 38.3175, "unit": "area_units"}

Answer: 38.3175

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+16 from x=-4.5 to x=-3.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.5)=31.75 and f(-3.2)=27.2.
The interval width is 1.3.


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

```python
def weighted_sum_001798(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_001798"}

Answer: python_code

Prompt: Write a Python function weighted_sum_001798(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_001798([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 15.05^2 and multiply by 0.5 * 23.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2706.7049, "unit": "J"}

Answer: 2706.7049

Prompt: A body of mass 23.9 kg moves at 15.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.05^2 and multiply by 0.5 * 23.9.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 19.2908, "unit": "state_units"}

Answer: 19.2908

Prompt: Use explicit Euler on dy/dt = -0.16 y with y(0)=28.5, step size h=0.2, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 618.0 / 100.
Final: {"answer": 6.18, "unit": "m"}

Answer: 6.18

Prompt: Convert 618 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 618.0 / 100.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.59 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 290.0259, "unit": "g"}

Answer: 290.0259

Prompt: A sample contains 6.59 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.59 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


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=0.1 and add it to the current value.
Final: {"answer": [-0.95, 0.515, 0.67], "unit": "temperature_units"}

Answer: -0.95

Answer: 0.515

Answer: 0.67

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=0.35; current interior values are [-1.55, 0.75, 0.7]. Use r=0.1. 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=0.1 and add it to the current value.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [-0.372, -0.621, 0.675], "unit": "temperature_units"}

Answer: -0.372

Answer: -0.621

Answer: 0.675

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=-0.15, right=2.7; current interior values are [-0.6, -0.45, -0.75]. Use r=0.38. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.38 and add it to the current value.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 11.4^2 and multiply by 0.5 * 9.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 594.567, "unit": "J"}

Answer: 594.567

Prompt: A body of mass 9.15 kg moves at 11.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.4^2 and multiply by 0.5 * 9.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3970 mL to 3.97 L.
3. Compute M = 1.375 / 3.97.
Final: {"answer": 0.3463, "unit": "mol/L"}

Answer: 0.3463

Prompt: A solution contains 1.375 mol of solute in 3970 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3970 mL to 3.97 L.
Compute M = 1.375 / 3.97.


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_001906(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_001906"}

Answer: python_code

Prompt: Write a Python function safe_mean_001906(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_001906([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1600 * 1.515 * 107.
Final: {"answer": 259368.0, "unit": "J"}

Answer: 259368.0

Prompt: A 1600 g sample has specific heat 1.515 J/(g*K). How much heat is needed to raise its temperature by 107 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1600 * 1.515 * 107.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3225 mL to 3.225 L.
3. Compute M = 2.075 / 3.225.
Final: {"answer": 0.6434, "unit": "mol/L"}

Answer: 0.6434

Prompt: A solution contains 2.075 mol of solute in 3225 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3225 mL to 3.225 L.
Compute M = 2.075 / 3.225.


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

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.73 y with y(0)=11, step size h=1.3, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.8)=20.7 and f(15.3)=58.2.
3. The interval width is 7.5.
Final: {"answer": 295.875, "unit": "area_units"}

Answer: 295.875

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+-18.3 from x=7.8 to x=15.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.8)=20.7 and f(15.3)=58.2.
The interval width is 7.5.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 4189.0 / 1000.
Final: {"answer": 4.189, "unit": "kg"}

Answer: 4.189

Prompt: Convert 4189 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 4189.0 / 1000.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.56 * 8.314 * 563 / 114.7.
Final: {"answer": 145.2797, "unit": "kPa"}

Answer: 145.2797

Prompt: An ideal gas sample has n=3.56 mol, T=563 K, and V=114.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.56 * 8.314 * 563 / 114.7.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 111.0 + 273.15.
Final: {"answer": 384.15, "unit": "K"}

Answer: 384.15

Prompt: Convert 111 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 111.0 + 273.15.


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 826578, 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. Mass equals amount in moles times molar mass.
2. Use m = 4.95 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 217.8495, "unit": "g"}

Answer: 217.8495

Prompt: A sample contains 4.95 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 = 4.95 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


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_001996(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_001996"}

Answer: python_code

Prompt: Write a Python function unit_vector_001996(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_001996(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 44.4^2 and multiply by 0.5 * 16.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16460.856, "unit": "J"}

Answer: 16460.856

Prompt: A body of mass 16.7 kg moves at 44.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.4^2 and multiply by 0.5 * 16.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.71 y with y(0)=55.5, step size h=1.45, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
Apply that update for 9 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)=28.83 and f(3.6)=-2.62.
3. The interval width is 8.5.
Final: {"answer": 111.3925, "unit": "area_units"}

Answer: 111.3925

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.7x+10.7 from x=-4.9 to x=3.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.9)=28.83 and f(3.6)=-2.62.
The interval width is 8.5.


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": [0.9, -8.75], "unit": "dimensionless"}

Answer: 0.9

Answer: -8.75

Prompt: A line passes through points (-13.5, -20.9) and (-6.75, -14.825). 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=60 degrees through the sine of 2 theta.
3. Substitute v=17.1 m/s and g=9.81 m/s^2.
Final: {"answer": 25.8139, "unit": "m"}

Answer: 25.8139

Prompt: A projectile is launched on level ground with no air resistance at speed 17.1 m/s and angle 60 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=60 degrees through the sine of 2 theta.
Substitute v=17.1 m/s and g=9.81 m/s^2.

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


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_002050(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_002050"}

Answer: python_code

Prompt: Write a Python function clamp_002050(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_002050(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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=65.3 m/s and g=9.81 m/s^2.
Final: {"answer": 134.3197, "unit": "m"}

Answer: 134.3197

Prompt: A projectile is launched on level ground with no air resistance at speed 65.3 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=65.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.62 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 362.3149, "unit": "g"}

Answer: 362.3149

Prompt: A sample contains 3.62 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 = 3.62 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.6)=39.54 and f(3)=-12.3.
3. The interval width is 9.6.
Final: {"answer": 130.752, "unit": "area_units"}

Answer: 130.752

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.4x+3.9 from x=-6.6 to x=3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.6)=39.54 and f(3)=-12.3.
The interval width is 9.6.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22645.0 / 1000.
Final: {"answer": 22.645, "unit": "kg"}

Answer: 22.645

Prompt: Convert 22645 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 22645.0 / 1000.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=658 mg, t=210.5 h, and T_half=41 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 18.7367, "unit": "mg"}

Answer: 18.7367

Prompt: A radioactive sample starts with 658 mg. Its half-life is 41 hours. How many mg remain after 210.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=658 mg, t=210.5 h, and T_half=41 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1620 mL to 1.62 L.
3. Compute M = 4.455 / 1.62.
Final: {"answer": 2.75, "unit": "mol/L"}

Answer: 2.75

Prompt: A solution contains 4.455 mol of solute in 1620 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1620 mL to 1.62 L.
Compute M = 4.455 / 1.62.


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": [-6.7, 9.75], "unit": "dimensionless"}

Answer: -6.7

Answer: 9.75

Prompt: A line passes through points (-2.5, 26.5) and (5.5, -27.1). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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=0.18 and interior values [-1.45, 2.25, 0.95], 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=32 degrees through the sine of 2 theta.
3. Substitute v=51.5 m/s and g=9.81 m/s^2.
Final: {"answer": 242.9996, "unit": "m"}

Answer: 242.9996

Prompt: A projectile is launched on level ground with no air resistance at speed 51.5 m/s and angle 32 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=32 degrees through the sine of 2 theta.
Substitute v=51.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 37.2244, "unit": "state_units"}

Answer: 37.2244

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=75.5, step size h=1.4, 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) = -0.15 y, so each step multiplies y by 1 - h*0.15.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4.6)=11.08 and f(2.5)=-23.
3. The interval width is 7.1.
Final: {"answer": -42.316, "unit": "area_units"}

Answer: -42.316

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.8x+-11 from x=-4.6 to x=2.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.6)=11.08 and f(2.5)=-23.
The interval width is 7.1.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 33.55^2 and multiply by 0.5 * 26.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 15054.9334, "unit": "J"}

Answer: 15054.9334

Prompt: A body of mass 26.75 kg moves at 33.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 33.55^2 and multiply by 0.5 * 26.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 300 mL to 0.3 L.
3. Compute M = 2.155 / 0.3.
Final: {"answer": 7.1833, "unit": "mol/L"}

Answer: 7.1833

Prompt: A solution contains 2.155 mol of solute in 300 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 300 mL to 0.3 L.
Compute M = 2.155 / 0.3.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=138 degrees and keep the unit as newtons.
Final: {"answer": [-124.8483, 112.4139], "unit": "N"}

Answer: -124.8483

Answer: 112.4139

Prompt: A vector has magnitude 168 N at 138 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=138 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In model card equation case 512665, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid warehouse sensor records in release 741417, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 39.85^2 and multiply by 0.5 * 14.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11394.0614, "unit": "J"}

Answer: 11394.0614

Prompt: A body of mass 14.35 kg moves at 39.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 39.85^2 and multiply by 0.5 * 14.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1395 * 4.105 * 48.
Final: {"answer": 274870.8, "unit": "J"}

Answer: 274870.8

Prompt: A 1395 g sample has specific heat 4.105 J/(g*K). How much heat is needed to raise its temperature by 48 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1395 * 4.105 * 48.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=34.4 V and R=167.8 ohm.
Final: {"answer": 7.0522, "unit": "W"}

Answer: 7.0522

Prompt: A resistor has resistance 167.8 ohm and voltage 34.4 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=34.4 V and R=167.8 ohm.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.4)=-14.68 and f(4.1)=-8.03.
3. The interval width is 9.5.
Final: {"answer": -107.8725, "unit": "area_units"}

Answer: -107.8725

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+-10.9 from x=-5.4 to x=4.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.4)=-14.68 and f(4.1)=-8.03.
The interval width is 9.5.


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 student derivation case 340013, 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. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.64 * 8.314 * 584 / 33.3.
Final: {"answer": 822.352, "unit": "kPa"}

Answer: 822.352

Prompt: An ideal gas sample has n=5.64 mol, T=584 K, and V=33.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.64 * 8.314 * 584 / 33.3.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 204.5 / 100.
Final: {"answer": 2.045, "unit": "m"}

Answer: 2.045

Prompt: Convert 204.5 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 204.5 / 100.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each laboratory sensor record from batch 28941 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. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4685 mL to 4.685 L.
3. Compute M = 1.57 / 4.685.
Final: {"answer": 0.3351, "unit": "mol/L"}

Answer: 0.3351

Prompt: A solution contains 1.57 mol of solute in 4685 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4685 mL to 4.685 L.
Compute M = 1.57 / 4.685.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.3 * 8.314 * 513 / 72.7.
Final: {"answer": 134.9338, "unit": "kPa"}

Answer: 134.9338

Prompt: An ideal gas sample has n=2.3 mol, T=513 K, and V=72.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.3 * 8.314 * 513 / 72.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1870 * 4.005 * 7.
Final: {"answer": 52425.45, "unit": "J"}

Answer: 52425.45

Prompt: A 1870 g sample has specific heat 4.005 J/(g*K). How much heat is needed to raise its temperature by 7 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1870 * 4.005 * 7.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4055 mL to 4.055 L.
3. Compute M = 2.24 / 4.055.
Final: {"answer": 0.5524, "unit": "mol/L"}

Answer: 0.5524

Prompt: A solution contains 2.24 mol of solute in 4055 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4055 mL to 4.055 L.
Compute M = 2.24 / 4.055.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 828.0 / 100.
Final: {"answer": 8.28, "unit": "m"}

Answer: 8.28

Prompt: Convert 828 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 828.0 / 100.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=690 mg, t=201 h, and T_half=120 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 216.0846, "unit": "mg"}

Answer: 216.0846

Prompt: A radioactive sample starts with 690 mg. Its half-life is 120 hours. How many mg remain after 201 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=690 mg, t=201 h, and T_half=120 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.8)=-48.62 and f(-1.8)=-27.02.
3. The interval width is 4.
Final: {"answer": -151.28, "unit": "area_units"}

Answer: -151.28

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.4x+-17.3 from x=-5.8 to x=-1.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.8)=-48.62 and f(-1.8)=-27.02.
The interval width is 4.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.95 kg and a = 12.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 100.5675, "unit": "N"}

Answer: 100.5675

Prompt: A cart has mass 7.95 kg and measured acceleration 12.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.95 kg and a = 12.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0024, "unit": "state_units"}

Answer: 0.0024

Prompt: Use explicit Euler on dy/dt = -0.8 y with y(0)=38, step size h=1.5, 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) = -0.8 y, so each step multiplies y by 1 - h*0.8.
Apply that update for 6 steps and round the final state.


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_002374(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_002374"}

Answer: python_code

Prompt: Write a Python function unit_vector_002374(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_002374(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=113 degrees and keep the unit as newtons.
Final: {"answer": [-42.5897, 100.335], "unit": "N"}

Answer: -42.5897

Answer: 100.335

Prompt: A vector has magnitude 109 N at 113 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=113 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 clamp_002392(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_002392"}

Answer: python_code

Prompt: Write a Python function clamp_002392(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_002392(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=15 degrees through the sine of 2 theta.
3. Substitute v=83.1 m/s and g=9.81 m/s^2.
Final: {"answer": 351.9679, "unit": "m"}

Answer: 351.9679

Prompt: A projectile is launched on level ground with no air resistance at speed 83.1 m/s and angle 15 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=15 degrees through the sine of 2 theta.
Substitute v=83.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=150 mg, t=256 h, and T_half=23 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0669, "unit": "mg"}

Answer: 0.0669

Prompt: A radioactive sample starts with 150 mg. Its half-life is 23 hours. How many mg remain after 256 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=150 mg, t=256 h, and T_half=23 h.
The remaining amount has the same mass unit as the initial amount.


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 sensor records in release 45215, 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 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 = 0.8 * 8.314 * 501 / 65.0.
Final: {"answer": 51.2654, "unit": "kPa"}

Answer: 51.2654

Prompt: An ideal gas sample has n=0.8 mol, T=501 K, and V=65.0 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 = 0.8 * 8.314 * 501 / 65.0.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-10)=-25.8 and f(-8)=-24.4.
3. The interval width is 2.
Final: {"answer": -50.2, "unit": "area_units"}

Answer: -50.2

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+-18.8 from x=-10 to x=-8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-10)=-25.8 and f(-8)=-24.4.
The interval width is 2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1410 * 3.31 * 40.
Final: {"answer": 186684.0, "unit": "J"}

Answer: 186684.0

Prompt: A 1410 g sample has specific heat 3.31 J/(g*K). How much heat is needed to raise its temperature by 40 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1410 * 3.31 * 40.


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=96.1 V and R=47.7 ohm.
Final: {"answer": 193.6103, "unit": "W"}

Answer: 193.6103

Prompt: A resistor has resistance 47.7 ohm and voltage 96.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=96.1 V and R=47.7 ohm.


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": [1.281, 0.112, 0.928], "unit": "temperature_units"}

Answer: 1.281

Answer: 0.112

Answer: 0.928

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=1.8, right=0.45; current interior values are [2.15, -1.45, 2.05]. 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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=637.5 mg, t=89.5 h, and T_half=21 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 33.2291, "unit": "mg"}

Answer: 33.2291

Prompt: A radioactive sample starts with 637.5 mg. Its half-life is 21 hours. How many mg remain after 89.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=637.5 mg, t=89.5 h, and T_half=21 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) = -0.29 y, so each step multiplies y by 1 - h*0.29.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 41.6902, "unit": "state_units"}

Answer: 41.6902

Prompt: Use explicit Euler on dy/dt = -0.29 y with y(0)=60, step size h=0.3, 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) = -0.29 y, so each step multiplies y by 1 - h*0.29.
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(8.9)=56.86 and f(14)=79.3.
3. The interval width is 5.1.
Final: {"answer": 347.208, "unit": "area_units"}

Answer: 347.208

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+17.7 from x=8.9 to x=14. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.9)=56.86 and f(14)=79.3.
The interval width is 5.1.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2103.5 / 100.
Final: {"answer": 21.035, "unit": "m"}

Answer: 21.035

Prompt: Convert 2103.5 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 2103.5 / 100.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.5^2 and multiply by 0.5 * 5.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2579.85, "unit": "J"}

Answer: 2579.85

Prompt: A body of mass 5.2 kg moves at 31.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.5^2 and multiply by 0.5 * 5.2.
The unit kg*m^2/s^2 is one joule.


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": [-0.15, -1.25], "unit": "dimensionless"}

Answer: -0.15

Answer: -1.25

Prompt: A line passes through points (7, -2.3) and (11.5, -2.975). 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. Use Newton's second law F = m a.
2. Substitute m = 9.2 kg and a = 5.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.9, "unit": "N"}

Answer: 52.9

Prompt: A cart has mass 9.2 kg and measured acceleration 5.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.2 kg and a = 5.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.43 * 8.314 * 451 / 1.8.
Final: {"answer": 11311.3356, "unit": "kPa"}

Answer: 11311.3356

Prompt: An ideal gas sample has n=5.43 mol, T=451 K, and V=1.8 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 = 5.43 * 8.314 * 451 / 1.8.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 4.6294, "unit": "state_units"}

Answer: 4.6294

Prompt: Use explicit Euler on dy/dt = -0.32 y with y(0)=10.5, step size h=1.05, for 2 steps. What is y after the final step?

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.65, 24.5], "unit": "dimensionless"}

Answer: -9.65

Answer: 24.5

Prompt: A line passes through points (7.5, -47.875) and (19, -158.85). 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 7.95^2 and multiply by 0.5 * 23.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 741.0493, "unit": "J"}

Answer: 741.0493

Prompt: A body of mass 23.45 kg moves at 7.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.95^2 and multiply by 0.5 * 23.45.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=799.5 mg, t=356.5 h, and T_half=117.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 97.6069, "unit": "mg"}

Answer: 97.6069

Prompt: A radioactive sample starts with 799.5 mg. Its half-life is 117.5 hours. How many mg remain after 356.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=799.5 mg, t=356.5 h, and T_half=117.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 18.15^2 and multiply by 0.5 * 7.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1194.1566, "unit": "J"}

Answer: 1194.1566

Prompt: A body of mass 7.25 kg moves at 18.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.15^2 and multiply by 0.5 * 7.25.
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 = 0.66 * 8.314 * 430 / 91.1.
Final: {"answer": 25.9003, "unit": "kPa"}

Answer: 25.9003

Prompt: An ideal gas sample has n=0.66 mol, T=430 K, and V=91.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.66 * 8.314 * 430 / 91.1.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 435.5 / 100.
Final: {"answer": 4.355, "unit": "m"}

Answer: 4.355

Prompt: Convert 435.5 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 435.5 / 100.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.3 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 189.243, "unit": "g"}

Answer: 189.243

Prompt: A sample contains 4.3 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 = 4.3 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


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 = 4.31 * 8.314 * 467 / 118.4.
Final: {"answer": 141.3359, "unit": "kPa"}

Answer: 141.3359

Prompt: An ideal gas sample has n=4.31 mol, T=467 K, and V=118.4 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 = 4.31 * 8.314 * 467 / 118.4.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=18 degrees through the sine of 2 theta.
3. Substitute v=64.1 m/s and g=9.81 m/s^2.
Final: {"answer": 246.1874, "unit": "m"}

Answer: 246.1874

Prompt: A projectile is launched on level ground with no air resistance at speed 64.1 m/s and angle 18 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=18 degrees through the sine of 2 theta.
Substitute v=64.1 m/s and g=9.81 m/s^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=0.2 and add it to the current value.
Final: {"answer": [-0.75, 0.5, 2.15], "unit": "temperature_units"}

Answer: -0.75

Answer: 0.5

Answer: 2.15

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=2.35; current interior values are [-1.9, 0.6, 2.6]. Use r=0.2. 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=0.2 and add it to the current value.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.05 kg and a = 6.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 134.335, "unit": "N"}

Answer: 134.335

Prompt: A cart has mass 20.05 kg and measured acceleration 6.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.05 kg and a = 6.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.2 * 8.314 * 616 / 4.8.
Final: {"answer": 213.3927, "unit": "kPa"}

Answer: 213.3927

Prompt: An ideal gas sample has n=0.2 mol, T=616 K, and V=4.8 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 = 0.2 * 8.314 * 616 / 4.8.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=226.5 mg, t=357.5 h, and T_half=35.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.2107, "unit": "mg"}

Answer: 0.2107

Prompt: A radioactive sample starts with 226.5 mg. Its half-life is 35.5 hours. How many mg remain after 357.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=226.5 mg, t=357.5 h, and T_half=35.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.29 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 953.0252, "unit": "g"}

Answer: 953.0252

Prompt: A sample contains 5.29 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 = 5.29 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 3915 mL to 3.915 L.
3. Compute M = 0.035 / 3.915.
Final: {"answer": 0.0089, "unit": "mol/L"}

Answer: 0.0089

Prompt: A solution contains 0.035 mol of solute in 3915 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3915 mL to 3.915 L.
Compute M = 0.035 / 3.915.


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": [4.7, 29.75], "unit": "dimensionless"}

Answer: 4.7

Answer: 29.75

Prompt: A line passes through points (-5.75, 2.725) and (-3.25, 14.475). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7 kg and a = 5.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 38.85, "unit": "N"}

Answer: 38.85

Prompt: A cart has mass 7 kg and measured acceleration 5.55 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 kg and a = 5.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4690 mL to 4.69 L.
3. Compute M = 1.815 / 4.69.
Final: {"answer": 0.387, "unit": "mol/L"}

Answer: 0.387

Prompt: A solution contains 1.815 mol of solute in 4690 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4690 mL to 4.69 L.
Compute M = 1.815 / 4.69.


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 = 1.46 * 8.314 * 332 / 107.9.
Final: {"answer": 37.349, "unit": "kPa"}

Answer: 37.349

Prompt: An ideal gas sample has n=1.46 mol, T=332 K, and V=107.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.46 * 8.314 * 332 / 107.9.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.85 kg and a = 3.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 62.205, "unit": "N"}

Answer: 62.205

Prompt: A cart has mass 18.85 kg and measured acceleration 3.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.85 kg and a = 3.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=178 degrees and keep the unit as newtons.
Final: {"answer": [-172.8946, 6.0376], "unit": "N"}

Answer: -172.8946

Answer: 6.0376

Prompt: A vector has magnitude 173 N at 178 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=178 degrees and keep the unit as newtons.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each warehouse invoice record from batch 218633 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 10618.0 / 1000.
Final: {"answer": 10.618, "unit": "kg"}

Answer: 10.618

Prompt: Convert 10618 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 10618.0 / 1000.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 41.2^2 and multiply by 0.5 * 2.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1909.62, "unit": "J"}

Answer: 1909.62

Prompt: A body of mass 2.25 kg moves at 41.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41.2^2 and multiply by 0.5 * 2.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2697.0 / 100.
Final: {"answer": 26.97, "unit": "m"}

Answer: 26.97

Prompt: Convert 2697 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 2697.0 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.75, 17.0], "unit": "dimensionless"}

Answer: -1.75

Answer: 17.0

Prompt: A line passes through points (9.5, 0.375) and (20.25, -18.4375). 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. 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=0.1 and add it to the current value.
Final: {"answer": [1.81, 0.4, 0.875], "unit": "temperature_units"}

Answer: 1.81

Answer: 0.4

Answer: 0.875

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=1.6, right=-0.55; current interior values are [2.05, 0.1, 1.15]. Use r=0.1. 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=0.1 and add it to the current value.


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

Answer: consistent

Prompt: In quality-control check case 624984, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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=69.8 m/s and g=9.81 m/s^2.
Final: {"answer": 248.3201, "unit": "m"}

Answer: 248.3201

Prompt: A projectile is launched on level ground with no air resistance at speed 69.8 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=69.8 m/s and g=9.81 m/s^2.


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=32.1 m/s and g=9.81 m/s^2.
Final: {"answer": 64.667, "unit": "m"}

Answer: 64.667

Prompt: A projectile is launched on level ground with no air resistance at speed 32.1 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=32.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.384, "unit": "state_units"}

Answer: 0.384

Prompt: Use explicit Euler on dy/dt = -0.73 y with y(0)=39.5, step size h=1.8, 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) = -0.73 y, so each step multiplies y by 1 - h*0.73.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=48 degrees and keep the unit as newtons.
Final: {"answer": [65.5748, 72.8282], "unit": "N"}

Answer: 65.5748

Answer: 72.8282

Prompt: A vector has magnitude 98 N at 48 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=48 degrees and keep the unit as newtons.


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 = 3.62 * 8.314 * 246 / 81.4.
Final: {"answer": 90.9556, "unit": "kPa"}

Answer: 90.9556

Prompt: An ideal gas sample has n=3.62 mol, T=246 K, and V=81.4 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 = 3.62 * 8.314 * 246 / 81.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1250 * 3.07 * 17.
Final: {"answer": 65237.5, "unit": "J"}

Answer: 65237.5

Prompt: A 1250 g sample has specific heat 3.07 J/(g*K). How much heat is needed to raise its temperature by 17 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1250 * 3.07 * 17.


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=114.5 V and R=7.5 ohm.
Final: {"answer": 1748.0333, "unit": "W"}

Answer: 1748.0333

Prompt: A resistor has resistance 7.5 ohm and voltage 114.5 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=114.5 V and R=7.5 ohm.


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 311445, 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. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1105 mL to 1.105 L.
3. Compute M = 1.305 / 1.105.
Final: {"answer": 1.181, "unit": "mol/L"}

Answer: 1.181

Prompt: A solution contains 1.305 mol of solute in 1105 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1105 mL to 1.105 L.
Compute M = 1.305 / 1.105.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(10)=-18.3 and f(18.9)=-30.76.
3. The interval width is 8.9.
Final: {"answer": -218.317, "unit": "area_units"}

Answer: -218.317

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+-4.3 from x=10 to x=18.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(10)=-18.3 and f(18.9)=-30.76.
The interval width is 8.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [0.378, 0.634, 0.465], "unit": "temperature_units"}

Answer: 0.378

Answer: 0.634

Answer: 0.465

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.1; current interior values are [-1.65, 2.35, -0.25]. Use r=0.26. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.26 and add it to the current value.


Response:
Reasoning:
1. 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 = 1.32 * 8.314 * 321 / 17.7.
Final: {"answer": 199.0287, "unit": "kPa"}

Answer: 199.0287

Prompt: An ideal gas sample has n=1.32 mol, T=321 K, and V=17.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.32 * 8.314 * 321 / 17.7.


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=89.9 V and R=20.4 ohm.
Final: {"answer": 396.177, "unit": "W"}

Answer: 396.177

Prompt: A resistor has resistance 20.4 ohm and voltage 89.9 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=89.9 V and R=20.4 ohm.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=33 degrees through the sine of 2 theta.
3. Substitute v=42.1 m/s and g=9.81 m/s^2.
Final: {"answer": 165.0537, "unit": "m"}

Answer: 165.0537

Prompt: A projectile is launched on level ground with no air resistance at speed 42.1 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=33 degrees through the sine of 2 theta.
Substitute v=42.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.56 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 256.2227, "unit": "g"}

Answer: 256.2227

Prompt: A sample contains 2.56 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.56 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 204.0 + 273.15.
Final: {"answer": 477.15, "unit": "K"}

Answer: 477.15

Prompt: Convert 204 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 204.0 + 273.15.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=678 mg, t=353 h, and T_half=70 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 20.5674, "unit": "mg"}

Answer: 20.5674

Prompt: A radioactive sample starts with 678 mg. Its half-life is 70 hours. How many mg remain after 353 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=678 mg, t=353 h, and T_half=70 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.4)=8.36 and f(6.5)=17.6.
3. The interval width is 2.1.
Final: {"answer": 27.258, "unit": "area_units"}

Answer: 27.258

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+-11 from x=4.4 to x=6.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.4)=8.36 and f(6.5)=17.6.
The interval width is 2.1.


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": [-5.2, -25.0], "unit": "dimensionless"}

Answer: -5.2

Answer: -25.0

Prompt: A line passes through points (-18.5, 71.2) and (-12.25, 38.7). Return [slope, intercept] for y = slope*x + intercept.

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


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=52.7 V and R=102.3 ohm.
Final: {"answer": 27.1485, "unit": "W"}

Answer: 27.1485

Prompt: A resistor has resistance 102.3 ohm and voltage 52.7 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=52.7 V and R=102.3 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3935 mL to 3.935 L.
3. Compute M = 3.345 / 3.935.
Final: {"answer": 0.8501, "unit": "mol/L"}

Answer: 0.8501

Prompt: A solution contains 3.345 mol of solute in 3935 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3935 mL to 3.935 L.
Compute M = 3.345 / 3.935.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 3.45^2 and multiply by 0.5 * 7.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 45.2295, "unit": "J"}

Answer: 45.2295

Prompt: A body of mass 7.6 kg moves at 3.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.45^2 and multiply by 0.5 * 7.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.98 * 8.314 * 443 / 16.4.
Final: {"answer": 1118.4054, "unit": "kPa"}

Answer: 1118.4054

Prompt: An ideal gas sample has n=4.98 mol, T=443 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 = 4.98 * 8.314 * 443 / 16.4.


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=158 V and R=88.9 ohm.
Final: {"answer": 280.8099, "unit": "W"}

Answer: 280.8099

Prompt: A resistor has resistance 88.9 ohm and voltage 158 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=158 V and R=88.9 ohm.


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": [-1.75, 20.5], "unit": "dimensionless"}

Answer: -1.75

Answer: 20.5

Prompt: A line passes through points (-16.25, 48.9375) and (-10, 38). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.95 kg and a = 0.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 1.6575, "unit": "N"}

Answer: 1.6575

Prompt: A cart has mass 1.95 kg and measured acceleration 0.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.95 kg and a = 0.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 22.1795, "unit": "state_units"}

Answer: 22.1795

Prompt: Use explicit Euler on dy/dt = -0.04 y with y(0)=23, step size h=0.45, 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) = -0.04 y, so each step multiplies y by 1 - h*0.04.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 17.45^2 and multiply by 0.5 * 9.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1423.5492, "unit": "J"}

Answer: 1423.5492

Prompt: A body of mass 9.35 kg moves at 17.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.45^2 and multiply by 0.5 * 9.35.
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 = 4.78 * 8.314 * 539 / 105.2.
Final: {"answer": 203.6156, "unit": "kPa"}

Answer: 203.6156

Prompt: An ideal gas sample has n=4.78 mol, T=539 K, and V=105.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.78 * 8.314 * 539 / 105.2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.84 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 384.3341, "unit": "g"}

Answer: 384.3341

Prompt: A sample contains 3.84 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 = 3.84 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 28.0653, "unit": "state_units"}

Answer: 28.0653

Prompt: Use explicit Euler on dy/dt = -0.01 y with y(0)=34, step size h=1.9, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=15 degrees through the sine of 2 theta.
3. Substitute v=14.9 m/s and g=9.81 m/s^2.
Final: {"answer": 11.3155, "unit": "m"}

Answer: 11.3155

Prompt: A projectile is launched on level ground with no air resistance at speed 14.9 m/s and angle 15 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=15 degrees through the sine of 2 theta.
Substitute v=14.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.65 * 8.314 * 554 / 82.4.
Final: {"answer": 204.026, "unit": "kPa"}

Answer: 204.026

Prompt: An ideal gas sample has n=3.65 mol, T=554 K, and V=82.4 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 = 3.65 * 8.314 * 554 / 82.4.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.01 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1.8016, "unit": "g"}

Answer: 1.8016

Prompt: A sample contains 0.01 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 = 0.01 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.4)=31.22 and f(-5.4)=22.02.
3. The interval width is 4.
Final: {"answer": 106.48, "unit": "area_units"}

Answer: 106.48

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.3x+9.6 from x=-9.4 to x=-5.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.4)=31.22 and f(-5.4)=22.02.
The interval width is 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=0.32 and add it to the current value.
Final: {"answer": [0.86, 0.002, 0.278], "unit": "temperature_units"}

Answer: 0.86

Answer: 0.002

Answer: 0.278

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.4; current interior values are [-1.7, 2.45, -1.05]. Use r=0.32. 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=0.32 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=341 degrees and keep the unit as newtons.
Final: {"answer": [34.0387, -11.7205], "unit": "N"}

Answer: 34.0387

Answer: -11.7205

Prompt: A vector has magnitude 36 N at 341 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=341 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.35, -9.75], "unit": "dimensionless"}

Answer: 7.35

Answer: -9.75

Prompt: A line passes through points (-15.5, -123.675) and (-10, -83.25). 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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.55 kg and a = 14.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 357.2025, "unit": "N"}

Answer: 357.2025

Prompt: A cart has mass 24.55 kg and measured acceleration 14.55 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 = 24.55 kg and a = 14.55 m/s^2.
The unit kg*m/s^2 is one newton.


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=93.5 V and R=7 ohm.
Final: {"answer": 1248.8929, "unit": "W"}

Answer: 1248.8929

Prompt: A resistor has resistance 7 ohm and voltage 93.5 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=93.5 V and R=7 ohm.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 22.0 + 273.15.
Final: {"answer": 295.15, "unit": "K"}

Answer: 295.15

Prompt: Convert 22 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 22.0 + 273.15.


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_003274(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003274"}

Answer: python_code

Prompt: Write a Python function clamp_003274(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_003274(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.59 * 8.314 * 321 / 36.0.
Final: {"answer": 192.0049, "unit": "kPa"}

Answer: 192.0049

Prompt: An ideal gas sample has n=2.59 mol, T=321 K, and V=36.0 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 = 2.59 * 8.314 * 321 / 36.0.


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": [2.65, -23.25], "unit": "dimensionless"}

Answer: 2.65

Answer: -23.25

Prompt: A line passes through points (0, -23.25) and (2, -17.95). 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. 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_003310(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_003310"}

Answer: python_code

Prompt: Write a Python function safe_mean_003310(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_003310([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=56 V and R=178.5 ohm.
Final: {"answer": 17.5686, "unit": "W"}

Answer: 17.5686

Prompt: A resistor has resistance 178.5 ohm and voltage 56 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=56 V and R=178.5 ohm.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.1)=22.28 and f(5.2)=36.56.
3. The interval width is 2.1.
Final: {"answer": 61.782, "unit": "area_units"}

Answer: 61.782

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.8x+1.2 from x=3.1 to x=5.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.1)=22.28 and f(5.2)=36.56.
The interval width is 2.1.


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

```python
def weighted_sum_003328(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_003328"}

Answer: python_code

Prompt: Write a Python function weighted_sum_003328(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_003328([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 6.45^2 and multiply by 0.5 * 20.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 416.025, "unit": "J"}

Answer: 416.025

Prompt: A body of mass 20 kg moves at 6.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.45^2 and multiply by 0.5 * 20.
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=35 degrees through the sine of 2 theta.
3. Substitute v=6.6 m/s and g=9.81 m/s^2.
Final: {"answer": 4.1726, "unit": "m"}

Answer: 4.1726

Prompt: A projectile is launched on level ground with no air resistance at speed 6.6 m/s and angle 35 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=35 degrees through the sine of 2 theta.
Substitute v=6.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=13 degrees and keep the unit as newtons.
Final: {"answer": [401.4405, 92.6798], "unit": "N"}

Answer: 401.4405

Answer: 92.6798

Prompt: A vector has magnitude 412 N at 13 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=13 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 820 * 1.065 * 104.
Final: {"answer": 90823.2, "unit": "J"}

Answer: 90823.2

Prompt: A 820 g sample has specific heat 1.065 J/(g*K). How much heat is needed to raise its temperature by 104 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 820 * 1.065 * 104.


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

Answer: consistent

Prompt: In simulation spec case 607967, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.15^2 and multiply by 0.5 * 25.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16.6966, "unit": "J"}

Answer: 16.6966

Prompt: A body of mass 25.25 kg moves at 1.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.15^2 and multiply by 0.5 * 25.25.
The unit kg*m^2/s^2 is one joule.