Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 1.8965, "unit": "state_units"}

Answer: 1.8965

Prompt: Use explicit Euler on dy/dt = -0.57 y with y(0)=56, step size h=0.55, 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) = -0.57 y, so each step multiplies y by 1 - h*0.57.
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(-7.5)=28.3 and f(1.7)=-21.38.
3. The interval width is 9.2.
Final: {"answer": 31.832, "unit": "area_units"}

Answer: 31.832

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.4x+-12.2 from x=-7.5 to x=1.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.5)=28.3 and f(1.7)=-21.38.
The interval width is 9.2.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.36 and add it to the current value.
Final: {"answer": [0.49, 0.574, -1.008], "unit": "temperature_units"}

Answer: 0.49

Answer: 0.574

Answer: -1.008

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.5, right=-1.9; current interior values are [2.65, -0.2, -0.9]. Use r=0.36. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.36 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 121.5 + 273.15.
Final: {"answer": 394.65, "unit": "K"}

Answer: 394.65

Prompt: Convert 121.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 121.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=330 degrees and keep the unit as newtons.
Final: {"answer": [307.872, -177.75], "unit": "N"}

Answer: 307.872

Answer: -177.75

Prompt: A vector has magnitude 355.5 N at 330 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=330 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.55, 5.25], "unit": "dimensionless"}

Answer: -7.55

Answer: 5.25

Prompt: A line passes through points (12, -85.35) and (20, -145.75). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 741237, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_005812(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_005812"}

Answer: python_code

Prompt: Write a Python function clamp_005812(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_005812(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=1.15 mol and T=603 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.55 kg and a = 3.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 82.9675, "unit": "N"}

Answer: 82.9675

Prompt: A cart has mass 21.55 kg and measured acceleration 3.85 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 = 21.55 kg and a = 3.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 16.05^2 and multiply by 0.5 * 20.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2595.3452, "unit": "J"}

Answer: 2595.3452

Prompt: A body of mass 20.15 kg moves at 16.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.05^2 and multiply by 0.5 * 20.15.
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 = 1950 * 4.175 * 48.
Final: {"answer": 390780.0, "unit": "J"}

Answer: 390780.0

Prompt: A 1950 g sample has specific heat 4.175 J/(g*K). How much heat is needed to raise its temperature by 48 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1950 * 4.175 * 48.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=52.4 V and R=149.5 ohm.
Final: {"answer": 18.3663, "unit": "W"}

Answer: 18.3663

Prompt: A resistor has resistance 149.5 ohm and voltage 52.4 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=52.4 V and R=149.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=711 mg, t=263.5 h, and T_half=41 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 8.2642, "unit": "mg"}

Answer: 8.2642

Prompt: A radioactive sample starts with 711 mg. Its half-life is 41 hours. How many mg remain after 263.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=711 mg, t=263.5 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. Mass equals amount in moles times molar mass.
2. Use m = 1.39 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 250.4168, "unit": "g"}

Answer: 250.4168

Prompt: A sample contains 1.39 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 = 1.39 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 4.9921, "unit": "state_units"}

Answer: 4.9921

Prompt: Use explicit Euler on dy/dt = -0.12 y with y(0)=70.5, step size h=1.65, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
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(2.1)=-2.57 and f(4.6)=-19.32.
3. The interval width is 2.5.
Final: {"answer": -27.3625, "unit": "area_units"}

Answer: -27.3625

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+11.5 from x=2.1 to x=4.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.1)=-2.57 and f(4.6)=-19.32.
The interval width is 2.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [2.13, -0.758, 0.722], "unit": "temperature_units"}

Answer: 2.13

Answer: -0.758

Answer: 0.722

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=-0.8; current interior values are [2.55, -1.1, 0.95]. Use r=0.06. 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=0.06 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 24445.0 / 1000.
Final: {"answer": 24.445, "unit": "kg"}

Answer: 24.445

Prompt: Convert 24445 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 24445.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.5, 22.5], "unit": "dimensionless"}

Answer: 5.5

Answer: 22.5

Prompt: A line passes through points (18.5, 124.25) and (30, 187.5). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def center_values_005830(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_005830"}

Answer: python_code

Prompt: Write a Python function center_values_005830(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_005830([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a segmentation scoring problem with 843 items and budget 71610, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.85 kg and a = 7.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 154.29, "unit": "N"}

Answer: 154.29

Prompt: A cart has mass 20.85 kg and measured acceleration 7.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.85 kg and a = 7.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 20.55^2 and multiply by 0.5 * 26.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5658.8535, "unit": "J"}

Answer: 5658.8535

Prompt: A body of mass 26.8 kg moves at 20.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 20.55^2 and multiply by 0.5 * 26.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=22 degrees through the sine of 2 theta.
3. Substitute v=15.8 m/s and g=9.81 m/s^2.
Final: {"answer": 17.6773, "unit": "m"}

Answer: 17.6773

Prompt: A projectile is launched on level ground with no air resistance at speed 15.8 m/s and angle 22 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=22 degrees through the sine of 2 theta.
Substitute v=15.8 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.58 * 8.314 * 464 / 100.9.
Final: {"answer": 22.1751, "unit": "kPa"}

Answer: 22.1751

Prompt: An ideal gas sample has n=0.58 mol, T=464 K, and V=100.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.58 * 8.314 * 464 / 100.9.


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=208.9 V and R=147.4 ohm.
Final: {"answer": 296.0598, "unit": "W"}

Answer: 296.0598

Prompt: A resistor has resistance 147.4 ohm and voltage 208.9 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=208.9 V and R=147.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=662 mg, t=72.5 h, and T_half=106 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 412.0641, "unit": "mg"}

Answer: 412.0641

Prompt: A radioactive sample starts with 662 mg. Its half-life is 106 hours. How many mg remain after 72.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=662 mg, t=72.5 h, and T_half=106 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.55 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1180.0218, "unit": "g"}

Answer: 1180.0218

Prompt: A sample contains 6.55 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.55 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 13.191, "unit": "state_units"}

Answer: 13.191

Prompt: Use explicit Euler on dy/dt = -0.83 y with y(0)=46, step size h=1.85, 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) = -0.83 y, so each step multiplies y by 1 - h*0.83.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-3.4)=8.18 and f(-3.1)=8.72.
3. The interval width is 0.3.
Final: {"answer": 2.535, "unit": "area_units"}

Answer: 2.535

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.8x+14.3 from x=-3.4 to x=-3.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.4)=8.18 and f(-3.1)=8.72.
The interval width is 0.3.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 24657.0 / 1000.
Final: {"answer": 24.657, "unit": "kg"}

Answer: 24.657

Prompt: Convert 24657 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 24657.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=169 degrees and keep the unit as newtons.
Final: {"answer": [-260.1312, 50.5644], "unit": "N"}

Answer: -260.1312

Answer: 50.5644

Prompt: A vector has magnitude 265 N at 169 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=169 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": [-7.45, 28.25], "unit": "dimensionless"}

Answer: -7.45

Answer: 28.25

Prompt: A line passes through points (2, 13.35) and (14.75, -81.6375). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In model card equation case 747565, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity divided by time is acceleration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
import math

def unit_vector_005848(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_005848"}

Answer: python_code

Prompt: Write a Python function unit_vector_005848(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_005848(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.75 kg and a = 11.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 55.8125, "unit": "N"}

Answer: 55.8125

Prompt: A cart has mass 4.75 kg and measured acceleration 11.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.75 kg and a = 11.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 6.6^2 and multiply by 0.5 * 25.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 559.746, "unit": "J"}

Answer: 559.746

Prompt: A body of mass 25.7 kg moves at 6.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.6^2 and multiply by 0.5 * 25.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=27 degrees through the sine of 2 theta.
3. Substitute v=60.1 m/s and g=9.81 m/s^2.
Final: {"answer": 297.8774, "unit": "m"}

Answer: 297.8774

Prompt: A projectile is launched on level ground with no air resistance at speed 60.1 m/s and angle 27 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=27 degrees through the sine of 2 theta.
Substitute v=60.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.37 * 8.314 * 253 / 48.4.
Final: {"answer": 189.9182, "unit": "kPa"}

Answer: 189.9182

Prompt: An ideal gas sample has n=4.37 mol, T=253 K, and V=48.4 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 = 4.37 * 8.314 * 253 / 48.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1940 * 4.16 * 84.
Final: {"answer": 677913.6, "unit": "J"}

Answer: 677913.6

Prompt: A 1940 g sample has specific heat 4.16 J/(g*K). How much heat is needed to raise its temperature by 84 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1940 * 4.16 * 84.


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=40.4 V and R=195.3 ohm.
Final: {"answer": 8.3572, "unit": "W"}

Answer: 8.3572

Prompt: A resistor has resistance 195.3 ohm and voltage 40.4 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=40.4 V and R=195.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=608.5 mg, t=233.5 h, and T_half=105.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 131.22, "unit": "mg"}

Answer: 131.22

Prompt: A radioactive sample starts with 608.5 mg. Its half-life is 105.5 hours. How many mg remain after 233.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=608.5 mg, t=233.5 h, and T_half=105.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.97 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 397.3454, "unit": "g"}

Answer: 397.3454

Prompt: A sample contains 3.97 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 = 3.97 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 830 mL to 0.83 L.
3. Compute M = 4.405 / 0.83.
Final: {"answer": 5.3072, "unit": "mol/L"}

Answer: 5.3072

Prompt: A solution contains 4.405 mol of solute in 830 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 830 mL to 0.83 L.
Compute M = 4.405 / 0.83.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.0006, "unit": "state_units"}

Answer: 0.0006

Prompt: Use explicit Euler on dy/dt = -0.58 y with y(0)=23.5, step size h=1.6, 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) = -0.58 y, so each step multiplies y by 1 - h*0.58.
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(-5.3)=0.09 and f(-2.7)=9.71.
3. The interval width is 2.6.
Final: {"answer": 12.74, "unit": "area_units"}

Answer: 12.74

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.7x+19.7 from x=-5.3 to x=-2.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.3)=0.09 and f(-2.7)=9.71.
The interval width is 2.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [2.266, -0.158, 0.024], "unit": "temperature_units"}

Answer: 2.266

Answer: -0.158

Answer: 0.024

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=2.85, right=-1.85; current interior values are [0.15, 2.05, -0.85]. Use r=0.46. Return the next interior vector.

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


Response:
Reasoning:
1. 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": [-115.9293, 4.0483], "unit": "N"}

Answer: -115.9293

Answer: 4.0483

Prompt: A vector has magnitude 116 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. 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, -27.0], "unit": "dimensionless"}

Answer: 2.65

Answer: -27.0

Prompt: A line passes through points (-18.5, -76.025) and (-14.25, -64.7625). 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 threshold_flags_005866(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_005866"}

Answer: python_code

Prompt: Write a Python function threshold_flags_005866(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_005866([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_005866([], 5) == []

assert threshold_flags_005866([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.65 kg and a = 1.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 42.2175, "unit": "N"}

Answer: 42.2175

Prompt: A cart has mass 21.65 kg and measured acceleration 1.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.65 kg and a = 1.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.25^2 and multiply by 0.5 * 14.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7080.0781, "unit": "J"}

Answer: 7080.0781

Prompt: A body of mass 14.5 kg moves at 31.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.25^2 and multiply by 0.5 * 14.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=47 degrees through the sine of 2 theta.
3. Substitute v=22.1 m/s and g=9.81 m/s^2.
Final: {"answer": 49.6657, "unit": "m"}

Answer: 49.6657

Prompt: A projectile is launched on level ground with no air resistance at speed 22.1 m/s and angle 47 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=47 degrees through the sine of 2 theta.
Substitute v=22.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.1 * 8.314 * 240 / 7.0.
Final: {"answer": 883.6594, "unit": "kPa"}

Answer: 883.6594

Prompt: An ideal gas sample has n=3.1 mol, T=240 K, and V=7.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.1 * 8.314 * 240 / 7.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1315 * 4.64 * 108.
Final: {"answer": 658972.8, "unit": "J"}

Answer: 658972.8

Prompt: A 1315 g sample has specific heat 4.64 J/(g*K). How much heat is needed to raise its temperature by 108 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1315 * 4.64 * 108.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=172.1 V and R=126 ohm.
Final: {"answer": 235.0667, "unit": "W"}

Answer: 235.0667

Prompt: A resistor has resistance 126 ohm and voltage 172.1 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=172.1 V and R=126 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=19 mg, t=52 h, and T_half=52.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 9.5629, "unit": "mg"}

Answer: 9.5629

Prompt: A radioactive sample starts with 19 mg. Its half-life is 52.5 hours. How many mg remain after 52 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=19 mg, t=52 h, and T_half=52.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.8 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 480.4176, "unit": "g"}

Answer: 480.4176

Prompt: A sample contains 4.8 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.8 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4680 mL to 4.68 L.
3. Compute M = 1.575 / 4.68.
Final: {"answer": 0.3365, "unit": "mol/L"}

Answer: 0.3365

Prompt: A solution contains 1.575 mol of solute in 4680 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4680 mL to 4.68 L.
Compute M = 1.575 / 4.68.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.95 y, so each step multiplies y by 1 - h*0.95.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.1519, "unit": "state_units"}

Answer: 0.1519

Prompt: Use explicit Euler on dy/dt = -0.95 y with y(0)=36, step size h=0.7, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.95 y, so each step multiplies y by 1 - h*0.95.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.2)=60.02 and f(-0.1)=4.51.
3. The interval width is 9.1.
Final: {"answer": 293.6115, "unit": "area_units"}

Answer: 293.6115

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.1x+3.9 from x=-9.2 to x=-0.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.2)=60.02 and f(-0.1)=4.51.
The interval width is 9.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.02 and add it to the current value.
Final: {"answer": [1.273, 0.015, 1.754], "unit": "temperature_units"}

Answer: 1.273

Answer: 0.015

Answer: 1.754

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=-1.1, right=1.35; current interior values are [1.35, -0.05, 1.8]. Use r=0.02. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.02 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 21985.0 / 1000.
Final: {"answer": 21.985, "unit": "kg"}

Answer: 21.985

Prompt: Convert 21985 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 21985.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=43 degrees and keep the unit as newtons.
Final: {"answer": [42.0528, 39.2149], "unit": "N"}

Answer: 42.0528

Answer: 39.2149

Prompt: A vector has magnitude 57.5 N at 43 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=43 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.9, -1.0], "unit": "dimensionless"}

Answer: -1.9

Answer: -1.0

Prompt: A line passes through points (10.75, -21.425) and (11.5, -22.85). 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. Compare the dimensions on both sides of the equation.
2. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 813207, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_005884(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_005884"}

Answer: python_code

Prompt: Write a Python function running_total_005884(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each warehouse survey record from batch 200223 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.75 kg and a = 6.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 24.375, "unit": "N"}

Answer: 24.375

Prompt: A cart has mass 3.75 kg and measured acceleration 6.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.75 kg and a = 6.5 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=12.3 V and R=189.5 ohm.
Final: {"answer": 0.7984, "unit": "W"}

Answer: 0.7984

Prompt: A resistor has resistance 189.5 ohm and voltage 12.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=12.3 V and R=189.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=790.5 mg, t=342.5 h, and T_half=65.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 21.0772, "unit": "mg"}

Answer: 21.0772

Prompt: A radioactive sample starts with 790.5 mg. Its half-life is 65.5 hours. How many mg remain after 342.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=790.5 mg, t=342.5 h, and T_half=65.5 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 = 2.08 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 374.7245, "unit": "g"}

Answer: 374.7245

Prompt: A sample contains 2.08 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.08 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 3170 mL to 3.17 L.
3. Compute M = 0.91 / 3.17.
Final: {"answer": 0.2871, "unit": "mol/L"}

Answer: 0.2871

Prompt: A solution contains 0.91 mol of solute in 3170 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3170 mL to 3.17 L.
Compute M = 0.91 / 3.17.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 3.2148, "unit": "state_units"}

Answer: 3.2148

Prompt: Use explicit Euler on dy/dt = -0.42 y with y(0)=41, step size h=0.95, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.4)=-20.2 and f(11.5)=-70.25.
3. The interval width is 9.1.
Final: {"answer": -411.5475, "unit": "area_units"}

Answer: -411.5475

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+-7 from x=2.4 to x=11.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.4)=-20.2 and f(11.5)=-70.25.
The interval width is 9.1.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 18964.0 / 1000.
Final: {"answer": 18.964, "unit": "kg"}

Answer: 18.964

Prompt: Convert 18964 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 18964.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=62 degrees and keep the unit as newtons.
Final: {"answer": [69.9513, 131.5592], "unit": "N"}

Answer: 69.9513

Answer: 131.5592

Prompt: A vector has magnitude 149 N at 62 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=62 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.05, 24.75], "unit": "dimensionless"}

Answer: 5.05

Answer: 24.75

Prompt: A line passes through points (-9.5, -23.225) and (-7, -10.6). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def pairwise_ratios_005902(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_005902"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_005902(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

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

try:
    pairwise_ratios_005902([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_005902([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.55 kg and a = 2.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 67.1175, "unit": "N"}

Answer: 67.1175

Prompt: A cart has mass 23.55 kg and measured acceleration 2.85 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 = 23.55 kg and a = 2.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 9.75^2 and multiply by 0.5 * 22.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1090.8422, "unit": "J"}

Answer: 1090.8422

Prompt: A body of mass 22.95 kg moves at 9.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.75^2 and multiply by 0.5 * 22.95.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=38 degrees through the sine of 2 theta.
3. Substitute v=64.8 m/s and g=9.81 m/s^2.
Final: {"answer": 415.3222, "unit": "m"}

Answer: 415.3222

Prompt: A projectile is launched on level ground with no air resistance at speed 64.8 m/s and angle 38 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=38 degrees through the sine of 2 theta.
Substitute v=64.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.22 * 8.314 * 411 / 77.0.
Final: {"answer": 54.1403, "unit": "kPa"}

Answer: 54.1403

Prompt: An ideal gas sample has n=1.22 mol, T=411 K, and V=77.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.22 * 8.314 * 411 / 77.0.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=45.1 V and R=18.6 ohm.
Final: {"answer": 109.3554, "unit": "W"}

Answer: 109.3554

Prompt: A resistor has resistance 18.6 ohm and voltage 45.1 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=45.1 V and R=18.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=519.5 mg, t=160 h, and T_half=66.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 98.0173, "unit": "mg"}

Answer: 98.0173

Prompt: A radioactive sample starts with 519.5 mg. Its half-life is 66.5 hours. How many mg remain after 160 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=519.5 mg, t=160 h, and T_half=66.5 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 = 0.01 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 0.5844, "unit": "g"}

Answer: 0.5844

Prompt: A sample contains 0.01 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.01 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 190 mL to 0.19 L.
3. Compute M = 4.97 / 0.19.
Final: {"answer": 26.1579, "unit": "mol/L"}

Answer: 26.1579

Prompt: A solution contains 4.97 mol of solute in 190 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 190 mL to 0.19 L.
Compute M = 4.97 / 0.19.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.72 y, so each step multiplies y by 1 - h*0.72.
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 = -0.72 y with y(0)=25, step size h=1.1, 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) = -0.72 y, so each step multiplies y by 1 - h*0.72.
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(3.4)=32.82 and f(11.3)=94.44.
3. The interval width is 7.9.
Final: {"answer": 502.677, "unit": "area_units"}

Answer: 502.677

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+6.3 from x=3.4 to x=11.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.4)=32.82 and f(11.3)=94.44.
The interval width is 7.9.


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=0.06 and add it to the current value.
Final: {"answer": [-1.611, -0.107, -1.195], "unit": "temperature_units"}

Answer: -1.611

Answer: -0.107

Answer: -1.195

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.55, right=1.25; current interior values are [-1.8, 0.1, -1.45]. Use r=0.06. 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=0.06 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2174.5 / 100.
Final: {"answer": 21.745, "unit": "m"}

Answer: 21.745

Prompt: Convert 2174.5 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 2174.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=4 degrees and keep the unit as newtons.
Final: {"answer": [473.8429, 33.1343], "unit": "N"}

Answer: 473.8429

Answer: 33.1343

Prompt: A vector has magnitude 475 N at 4 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=4 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": [7.45, -22.0], "unit": "dimensionless"}

Answer: 7.45

Answer: -22.0

Prompt: A line passes through points (4.75, 13.3875) and (16.25, 99.0625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In sensor calibration case 59944, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a routing scoring problem with 4891 items and budget 88220, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 6.1^2 and multiply by 0.5 * 2.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 39.0705, "unit": "J"}

Answer: 39.0705

Prompt: A body of mass 2.1 kg moves at 6.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.1^2 and multiply by 0.5 * 2.1.
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=22 degrees through the sine of 2 theta.
3. Substitute v=36.6 m/s and g=9.81 m/s^2.
Final: {"answer": 94.8559, "unit": "m"}

Answer: 94.8559

Prompt: A projectile is launched on level ground with no air resistance at speed 36.6 m/s and angle 22 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=22 degrees through the sine of 2 theta.
Substitute v=36.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.18 * 8.314 * 264 / 86.8.
Final: {"answer": 105.6989, "unit": "kPa"}

Answer: 105.6989

Prompt: An ideal gas sample has n=4.18 mol, T=264 K, and V=86.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.18 * 8.314 * 264 / 86.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 815 * 4.63 * 50.
Final: {"answer": 188672.5, "unit": "J"}

Answer: 188672.5

Prompt: A 815 g sample has specific heat 4.63 J/(g*K). How much heat is needed to raise its temperature by 50 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 815 * 4.63 * 50.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=786.5 mg, t=90 h, and T_half=60.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 280.4694, "unit": "mg"}

Answer: 280.4694

Prompt: A radioactive sample starts with 786.5 mg. Its half-life is 60.5 hours. How many mg remain after 90 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=786.5 mg, t=90 h, and T_half=60.5 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) = -0.6 y, so each step multiplies y by 1 - h*0.6.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 5.1904, "unit": "state_units"}

Answer: 5.1904

Prompt: Use explicit Euler on dy/dt = -0.6 y with y(0)=14, step size h=0.3, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.
Apply that update for 5 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)=-12.4 and f(-3.4)=-13.12.
3. The interval width is 0.6.
Final: {"answer": -7.656, "unit": "area_units"}

Answer: -7.656

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.2x+-17.2 from x=-4 to x=-3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4)=-12.4 and f(-3.4)=-13.12.
The interval width is 0.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [1.112, 0.15, 0.996], "unit": "temperature_units"}

Answer: 1.112

Answer: 0.15

Answer: 0.996

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=1.95, right=1.4; current interior values are [-0.45, 0.7, 0.6]. Use r=0.44. 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=0.44 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 6.0 + 273.15.
Final: {"answer": 279.15, "unit": "K"}

Answer: 279.15

Prompt: Convert 6 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 6.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=324 degrees and keep the unit as newtons.
Final: {"answer": [306.2129, -222.4767], "unit": "N"}

Answer: 306.2129

Answer: -222.4767

Prompt: A vector has magnitude 378.5 N at 324 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=324 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
import math

def unit_vector_005938(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_005938"}

Answer: python_code

Prompt: Write a Python function unit_vector_005938(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_005938(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: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=33 and h=1.55, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 19.7 kg and a = 6.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 130.02, "unit": "N"}

Answer: 130.02

Prompt: A cart has mass 19.7 kg and measured acceleration 6.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 19.7 kg and a = 6.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 42.2^2 and multiply by 0.5 * 15.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13979.594, "unit": "J"}

Answer: 13979.594

Prompt: A body of mass 15.7 kg moves at 42.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.2^2 and multiply by 0.5 * 15.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=82 degrees through the sine of 2 theta.
3. Substitute v=20.7 m/s and g=9.81 m/s^2.
Final: {"answer": 12.0395, "unit": "m"}

Answer: 12.0395

Prompt: A projectile is launched on level ground with no air resistance at speed 20.7 m/s and angle 82 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=82 degrees through the sine of 2 theta.
Substitute v=20.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1200 * 2.55 * 107.
Final: {"answer": 327420.0, "unit": "J"}

Answer: 327420.0

Prompt: A 1200 g sample has specific heat 2.55 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 = 1200 * 2.55 * 107.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=79.7 V and R=159.4 ohm.
Final: {"answer": 39.85, "unit": "W"}

Answer: 39.85

Prompt: A resistor has resistance 159.4 ohm and voltage 79.7 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=79.7 V and R=159.4 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.96 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 696.6055, "unit": "g"}

Answer: 696.6055

Prompt: A sample contains 6.96 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.96 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1980 mL to 1.98 L.
3. Compute M = 3.175 / 1.98.
Final: {"answer": 1.6035, "unit": "mol/L"}

Answer: 1.6035

Prompt: A solution contains 3.175 mol of solute in 1980 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1980 mL to 1.98 L.
Compute M = 3.175 / 1.98.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.4889, "unit": "state_units"}

Answer: 0.4889

Prompt: Use explicit Euler on dy/dt = -0.67 y with y(0)=28, step size h=0.95, 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) = -0.67 y, so each step multiplies y by 1 - h*0.67.
Apply that update for 4 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=0.02 and add it to the current value.
Final: {"answer": [-1.89, -1.891, 0.941], "unit": "temperature_units"}

Answer: -1.89

Answer: -1.891

Answer: 0.941

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=1; current interior values are [-1.95, -1.95, 1.0]. Use r=0.02. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.02 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 358.5 / 100.
Final: {"answer": 3.585, "unit": "m"}

Answer: 3.585

Prompt: Convert 358.5 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 358.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=341 degrees and keep the unit as newtons.
Final: {"answer": [85.0967, -29.3011], "unit": "N"}

Answer: 85.0967

Answer: -29.3011

Prompt: A vector has magnitude 90 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": [5.85, 4.25], "unit": "dimensionless"}

Answer: 5.85

Answer: 4.25

Prompt: A line passes through points (-5.25, -26.4625) and (-1.5, -4.525). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In lab notebook case 285011, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def threshold_flags_005956(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_005956"}

Answer: python_code

Prompt: Write a Python function threshold_flags_005956(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_005956([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_005956([], 5) == []

assert threshold_flags_005956([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 23.9 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 = 17.45 kg and a = 9.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 159.6675, "unit": "N"}

Answer: 159.6675

Prompt: A cart has mass 17.45 kg and measured acceleration 9.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.45 kg and a = 9.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.14 * 8.314 * 443 / 48.8.
Final: {"answer": 86.0397, "unit": "kPa"}

Answer: 86.0397

Prompt: An ideal gas sample has n=1.14 mol, T=443 K, and V=48.8 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 = 1.14 * 8.314 * 443 / 48.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 470 * 2.965 * 14.
Final: {"answer": 19509.7, "unit": "J"}

Answer: 19509.7

Prompt: A 470 g sample has specific heat 2.965 J/(g*K). How much heat is needed to raise its temperature by 14 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 470 * 2.965 * 14.


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=48 V and R=50.7 ohm.
Final: {"answer": 45.4438, "unit": "W"}

Answer: 45.4438

Prompt: A resistor has resistance 50.7 ohm and voltage 48 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=48 V and R=50.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=933.5 mg, t=150.5 h, and T_half=112 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 367.7945, "unit": "mg"}

Answer: 367.7945

Prompt: A radioactive sample starts with 933.5 mg. Its half-life is 112 hours. How many mg remain after 150.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=933.5 mg, t=150.5 h, and T_half=112 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) = -0.61 y, so each step multiplies y by 1 - h*0.61.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.1327, "unit": "state_units"}

Answer: 0.1327

Prompt: Use explicit Euler on dy/dt = -0.61 y with y(0)=1.5, step size h=0.3, 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) = -0.61 y, so each step multiplies y by 1 - h*0.61.
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(-5.5)=8.4 and f(2.3)=13.08.
3. The interval width is 7.8.
Final: {"answer": 83.772, "unit": "area_units"}

Answer: 83.772

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+11.7 from x=-5.5 to x=2.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.5)=8.4 and f(2.3)=13.08.
The interval width is 7.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.24 and add it to the current value.
Final: {"answer": [-0.842, -0.612, -0.324], "unit": "temperature_units"}

Answer: -0.842

Answer: -0.612

Answer: -0.324

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.5, right=0.55; current interior values are [-0.65, -0.6, -0.6]. Use r=0.24. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.24 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -37.5 + 273.15.
Final: {"answer": 235.65, "unit": "K"}

Answer: 235.65

Prompt: Convert -37.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute -37.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=16 degrees and keep the unit as newtons.
Final: {"answer": [254.7343, 73.0439], "unit": "N"}

Answer: 254.7343

Answer: 73.0439

Prompt: A vector has magnitude 265 N at 16 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=16 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": [0.6, -20.0], "unit": "dimensionless"}

Answer: 0.6

Answer: -20.0

Prompt: A line passes through points (4, -17.6) and (11.25, -13.25). 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. 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 585118, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_005974(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_005974"}

Answer: python_code

Prompt: Write a Python function weighted_sum_005974(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_005974([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 = 14.3^2 and multiply by 0.5 * 20.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2060.2368, "unit": "J"}

Answer: 2060.2368

Prompt: A body of mass 20.15 kg moves at 14.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14.3^2 and multiply by 0.5 * 20.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=74 degrees through the sine of 2 theta.
3. Substitute v=77.9 m/s and g=9.81 m/s^2.
Final: {"answer": 327.805, "unit": "m"}

Answer: 327.805

Prompt: A projectile is launched on level ground with no air resistance at speed 77.9 m/s and angle 74 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=74 degrees through the sine of 2 theta.
Substitute v=77.9 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 = 1.09 * 8.314 * 591 / 113.4.
Final: {"answer": 47.2292, "unit": "kPa"}

Answer: 47.2292

Prompt: An ideal gas sample has n=1.09 mol, T=591 K, and V=113.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.09 * 8.314 * 591 / 113.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1150 * 1.325 * 48.
Final: {"answer": 73140.0, "unit": "J"}

Answer: 73140.0

Prompt: A 1150 g sample has specific heat 1.325 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 = 1150 * 1.325 * 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=229 V and R=114.9 ohm.
Final: {"answer": 456.4056, "unit": "W"}

Answer: 456.4056

Prompt: A resistor has resistance 114.9 ohm and voltage 229 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=229 V and R=114.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=754.5 mg, t=206 h, and T_half=42 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 25.1871, "unit": "mg"}

Answer: 25.1871

Prompt: A radioactive sample starts with 754.5 mg. Its half-life is 42 hours. How many mg remain after 206 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=754.5 mg, t=206 h, and T_half=42 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.07 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 267.1407, "unit": "g"}

Answer: 267.1407

Prompt: A sample contains 6.07 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 = 6.07 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 230 mL to 0.23 L.
3. Compute M = 4.78 / 0.23.
Final: {"answer": 20.7826, "unit": "mol/L"}

Answer: 20.7826

Prompt: A solution contains 4.78 mol of solute in 230 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 230 mL to 0.23 L.
Compute M = 4.78 / 0.23.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.2)=-19.9 and f(-8.1)=-19.7.
3. The interval width is 0.1.
Final: {"answer": -1.98, "unit": "area_units"}

Answer: -1.98

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2x+-3.5 from x=-8.2 to x=-8.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.2)=-19.9 and f(-8.1)=-19.7.
The interval width is 0.1.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=159 degrees and keep the unit as newtons.
Final: {"answer": [-352.4266, 135.2839], "unit": "N"}

Answer: -352.4266

Answer: 135.2839

Prompt: A vector has magnitude 377.5 N at 159 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=159 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.0, 6.25], "unit": "dimensionless"}

Answer: 1.0

Answer: 6.25

Prompt: A line passes through points (-4.25, 2) and (9.5, 15.75). Return [slope, intercept] for y = slope*x + intercept.

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


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_005992(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_005992"}

Answer: python_code

Prompt: Write a Python function unit_vector_005992(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_005992(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a scheduler scoring problem with 4853 items and budget 96495, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.6 kg and a = 10.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 150.38, "unit": "N"}

Answer: 150.38

Prompt: A cart has mass 14.6 kg and measured acceleration 10.3 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 = 14.6 kg and a = 10.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 11.5^2 and multiply by 0.5 * 26.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1772.15, "unit": "J"}

Answer: 1772.15

Prompt: A body of mass 26.8 kg moves at 11.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.5^2 and multiply by 0.5 * 26.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=114.4 V and R=129.5 ohm.
Final: {"answer": 101.0607, "unit": "W"}

Answer: 101.0607

Prompt: A resistor has resistance 129.5 ohm and voltage 114.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=114.4 V and R=129.5 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3610 mL to 3.61 L.
3. Compute M = 0.31 / 3.61.
Final: {"answer": 0.0859, "unit": "mol/L"}

Answer: 0.0859

Prompt: A solution contains 0.31 mol of solute in 3610 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3610 mL to 3.61 L.
Compute M = 0.31 / 3.61.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0227, "unit": "state_units"}

Answer: 0.0227

Prompt: Use explicit Euler on dy/dt = -0.37 y with y(0)=74.5, step size h=1.5, 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) = -0.37 y, so each step multiplies y by 1 - h*0.37.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.5)=47.45 and f(17)=90.2.
3. The interval width is 9.5.
Final: {"answer": 653.8375, "unit": "area_units"}

Answer: 653.8375

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.5x+13.7 from x=7.5 to x=17. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.5)=47.45 and f(17)=90.2.
The interval width is 9.5.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 33527.0 / 1000.
Final: {"answer": 33.527, "unit": "kg"}

Answer: 33.527

Prompt: Convert 33527 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 33527.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=354 degrees and keep the unit as newtons.
Final: {"answer": [411.2348, -43.2225], "unit": "N"}

Answer: 411.2348

Answer: -43.2225

Prompt: A vector has magnitude 413.5 N at 354 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=354 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.25, 18.75], "unit": "dimensionless"}

Answer: -6.25

Answer: 18.75

Prompt: A line passes through points (16.5, -84.375) and (20.25, -107.812). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In model card equation case 838650, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def weighted_sum_006010(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_006010"}

Answer: python_code

Prompt: Write a Python function weighted_sum_006010(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_006010([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.94 mol and T=606 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18 kg and a = 0.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 17.1, "unit": "N"}

Answer: 17.1

Prompt: A cart has mass 18 kg and measured acceleration 0.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18 kg and a = 0.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=19 degrees through the sine of 2 theta.
3. Substitute v=8.1 m/s and g=9.81 m/s^2.
Final: {"answer": 4.1176, "unit": "m"}

Answer: 4.1176

Prompt: A projectile is launched on level ground with no air resistance at speed 8.1 m/s and angle 19 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=19 degrees through the sine of 2 theta.
Substitute v=8.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.1 * 8.314 * 444 / 44.9.
Final: {"answer": 8.2214, "unit": "kPa"}

Answer: 8.2214

Prompt: An ideal gas sample has n=0.1 mol, T=444 K, and V=44.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.1 * 8.314 * 444 / 44.9.


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=23.6 V and R=28.4 ohm.
Final: {"answer": 19.6113, "unit": "W"}

Answer: 19.6113

Prompt: A resistor has resistance 28.4 ohm and voltage 23.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=23.6 V and R=28.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=289.5 mg, t=318 h, and T_half=2.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 289.5 mg. Its half-life is 2.5 hours. How many mg remain after 318 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=289.5 mg, t=318 h, and T_half=2.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4715 mL to 4.715 L.
3. Compute M = 1.84 / 4.715.
Final: {"answer": 0.3902, "unit": "mol/L"}

Answer: 0.3902

Prompt: A solution contains 1.84 mol of solute in 4715 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4715 mL to 4.715 L.
Compute M = 1.84 / 4.715.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.79 y with y(0)=20.5, step size h=1.05, 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) = -0.79 y, so each step multiplies y by 1 - h*0.79.
Apply that update for 10 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=0.02 and add it to the current value.
Final: {"answer": [-0.987, 0.742, -0.216], "unit": "temperature_units"}

Answer: -0.987

Answer: 0.742

Answer: -0.216

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.25, right=0.4; current interior values are [-1.05, 0.8, -0.25]. Use r=0.02. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.02 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 35068.0 / 1000.
Final: {"answer": 35.068, "unit": "kg"}

Answer: 35.068

Prompt: Convert 35068 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 35068.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=113 degrees and keep the unit as newtons.
Final: {"answer": [-135.3883, 318.9549], "unit": "N"}

Answer: -135.3883

Answer: 318.9549

Prompt: A vector has magnitude 346.5 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 slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.8, 9.5], "unit": "dimensionless"}

Answer: -6.8

Answer: 9.5

Prompt: A line passes through points (-18.5, 135.3) and (-17.75, 130.2). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In sensor calibration case 835540, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_006028(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_006028"}

Answer: python_code

Prompt: Write a Python function unit_vector_006028(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_006028(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.1 kg and a = 0.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 2.13, "unit": "N"}

Answer: 2.13

Prompt: A cart has mass 7.1 kg and measured acceleration 0.3 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 = 7.1 kg and a = 0.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 2.7^2 and multiply by 0.5 * 7.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 26.0618, "unit": "J"}

Answer: 26.0618

Prompt: A body of mass 7.15 kg moves at 2.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.7^2 and multiply by 0.5 * 7.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.02 * 8.314 * 464 / 105.9.
Final: {"answer": 146.4395, "unit": "kPa"}

Answer: 146.4395

Prompt: An ideal gas sample has n=4.02 mol, T=464 K, and V=105.9 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 = 4.02 * 8.314 * 464 / 105.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1005 * 1.595 * 101.
Final: {"answer": 161900.475, "unit": "J"}

Answer: 161900.475

Prompt: A 1005 g sample has specific heat 1.595 J/(g*K). How much heat is needed to raise its temperature by 101 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1005 * 1.595 * 101.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=77.4 V and R=98.3 ohm.
Final: {"answer": 60.9436, "unit": "W"}

Answer: 60.9436

Prompt: A resistor has resistance 98.3 ohm and voltage 77.4 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=77.4 V and R=98.3 ohm.