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_007324(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_007324"}

Answer: python_code

Prompt: Write a Python function unit_vector_007324(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_007324(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=177 degrees and keep the unit as newtons.
Final: {"answer": [-489.3285, 25.6446], "unit": "N"}

Answer: -489.3285

Answer: 25.6446

Prompt: A vector has magnitude 490 N at 177 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=177 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": [-8.15, -4.5], "unit": "dimensionless"}

Answer: -8.15

Answer: -4.5

Prompt: A line passes through points (15.25, -128.788) and (16.25, -136.938). 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 43.0 + 273.15.
Final: {"answer": 316.15, "unit": "K"}

Answer: 316.15

Prompt: Convert 43 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 43.0 + 273.15.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.5 kg and a = 12.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 289.125, "unit": "N"}

Answer: 289.125

Prompt: A cart has mass 22.5 kg and measured acceleration 12.85 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 = 22.5 kg and a = 12.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=461 mg, t=15 h, and T_half=100.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 415.6914, "unit": "mg"}

Answer: 415.6914

Prompt: A radioactive sample starts with 461 mg. Its half-life is 100.5 hours. How many mg remain after 15 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=461 mg, t=15 h, and T_half=100.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. 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 = 4.54 * 8.314 * 348 / 110.9.
Final: {"answer": 118.4441, "unit": "kPa"}

Answer: 118.4441

Prompt: An ideal gas sample has n=4.54 mol, T=348 K, and V=110.9 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 = 4.54 * 8.314 * 348 / 110.9.


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_007414(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007414"}

Answer: python_code

Prompt: Write a Python function running_total_007414(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. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.8 * 8.314 * 320 / 31.0.
Final: {"answer": 240.3014, "unit": "kPa"}

Answer: 240.3014

Prompt: An ideal gas sample has n=2.8 mol, T=320 K, and V=31.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.8 * 8.314 * 320 / 31.0.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=333 mg, t=156 h, and T_half=77.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 82.5087, "unit": "mg"}

Answer: 82.5087

Prompt: A radioactive sample starts with 333 mg. Its half-life is 77.5 hours. How many mg remain after 156 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=333 mg, t=156 h, and T_half=77.5 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 2575 mL to 2.575 L.
3. Compute M = 1.78 / 2.575.
Final: {"answer": 0.6913, "unit": "mol/L"}

Answer: 0.6913

Prompt: A solution contains 1.78 mol of solute in 2575 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2575 mL to 2.575 L.
Compute M = 1.78 / 2.575.


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=79.3 V and R=7 ohm.
Final: {"answer": 898.3557, "unit": "W"}

Answer: 898.3557

Prompt: A resistor has resistance 7 ohm and voltage 79.3 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=79.3 V and R=7 ohm.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=280 degrees and keep the unit as newtons.
Final: {"answer": [42.3702, -240.2931], "unit": "N"}

Answer: 42.3702

Answer: -240.2931

Prompt: A vector has magnitude 244 N at 280 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=280 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.65 kg and a = 1.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 11.0975, "unit": "N"}

Answer: 11.0975

Prompt: A cart has mass 9.65 kg and measured acceleration 1.15 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 = 9.65 kg and a = 1.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [-0.109, -1.123, -0.246], "unit": "temperature_units"}

Answer: -0.109

Answer: -1.123

Answer: -0.246

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=0.95; current interior values are [-0.55, -0.85, -1.8]. Use r=0.42. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.42 and add it to the current value.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.95, 29.5], "unit": "dimensionless"}

Answer: -8.95

Answer: 29.5

Prompt: A line passes through points (9.75, -57.7625) and (13.75, -93.5625). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=22 degrees through the sine of 2 theta.
3. Substitute v=36.2 m/s and g=9.81 m/s^2.
Final: {"answer": 92.7939, "unit": "m"}

Answer: 92.7939

Prompt: A projectile is launched on level ground with no air resistance at speed 36.2 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=36.2 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=504.5 mg, t=53 h, and T_half=66 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 289.1512, "unit": "mg"}

Answer: 289.1512

Prompt: A radioactive sample starts with 504.5 mg. Its half-life is 66 hours. How many mg remain after 53 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=504.5 mg, t=53 h, and T_half=66 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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)=47.5 and h=0.15, 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. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.12 and add it to the current value.
Final: {"answer": [0.754, -0.72, 0.896], "unit": "temperature_units"}

Answer: 0.754

Answer: -0.72

Answer: 0.896

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=2.25, right=-1.95; current interior values are [0.85, -1.35, 1.7]. Use r=0.12. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 682.0 / 1000.
Final: {"answer": 0.682, "unit": "kg"}

Answer: 0.682

Prompt: Convert 682 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 682.0 / 1000.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In simulation spec case 618226, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=85 degrees through the sine of 2 theta.
3. Substitute v=12.6 m/s and g=9.81 m/s^2.
Final: {"answer": 2.8102, "unit": "m"}

Answer: 2.8102

Prompt: A projectile is launched on level ground with no air resistance at speed 12.6 m/s and angle 85 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=85 degrees through the sine of 2 theta.
Substitute v=12.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=47 degrees through the sine of 2 theta.
3. Substitute v=38.7 m/s and g=9.81 m/s^2.
Final: {"answer": 152.2978, "unit": "m"}

Answer: 152.2978

Prompt: A projectile is launched on level ground with no air resistance at speed 38.7 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=38.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=174 degrees and keep the unit as newtons.
Final: {"answer": [-221.7784, 23.3098], "unit": "N"}

Answer: -221.7784

Answer: 23.3098

Prompt: A vector has magnitude 223 N at 174 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=174 degrees and keep the unit as newtons.


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

```python
def normalize_007666(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_007666"}

Answer: python_code

Prompt: Write a Python function normalize_007666(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_007666([2, 3, 5]); assert len(out) == 3

try:
    normalize_007666([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 registry experiment record from batch 15164 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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.2)=30.46 and f(7.1)=47.23.
3. The interval width is 3.9.
Final: {"answer": 151.4955, "unit": "area_units"}

Answer: 151.4955

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.3x+16.7 from x=3.2 to x=7.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.2)=30.46 and f(7.1)=47.23.
The interval width is 3.9.

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


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=75.5 V and R=78.6 ohm.
Final: {"answer": 72.5223, "unit": "W"}

Answer: 72.5223

Prompt: A resistor has resistance 78.6 ohm and voltage 75.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=75.5 V and R=78.6 ohm.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 11.45 kg and a = 1.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 20.61, "unit": "N"}

Answer: 20.61

Prompt: A cart has mass 11.45 kg and measured acceleration 1.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 11.45 kg and a = 1.8 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.5 kg and a = 14.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 94.575, "unit": "N"}

Answer: 94.575

Prompt: A cart has mass 6.5 kg and measured acceleration 14.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.5 kg and a = 14.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2405 mL to 2.405 L.
3. Compute M = 1.185 / 2.405.
Final: {"answer": 0.4927, "unit": "mol/L"}

Answer: 0.4927

Prompt: A solution contains 1.185 mol of solute in 2405 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2405 mL to 2.405 L.
Compute M = 1.185 / 2.405.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 3.2634, "unit": "state_units"}

Answer: 3.2634

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=8, step size h=0.8, 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-0.7)=13.34 and f(7.8)=62.64.
3. The interval width is 8.5.
Final: {"answer": 322.915, "unit": "area_units"}

Answer: 322.915

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.8x+17.4 from x=-0.7 to x=7.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.7)=13.34 and f(7.8)=62.64.
The interval width is 8.5.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.55, -9.0], "unit": "dimensionless"}

Answer: 6.55

Answer: -9.0

Prompt: A line passes through points (-0.75, -13.9125) and (1.25, -0.8125). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.12 and add it to the current value.
Final: {"answer": [-1.14, 0.644, 2.06], "unit": "temperature_units"}

Answer: -1.14

Answer: 0.644

Answer: 2.06

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-0.9; current interior values are [-1.5, 0.65, 2.75]. Use r=0.12. Return the next interior vector.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [-0.652, -1.306, 0.013], "unit": "temperature_units"}

Answer: -0.652

Answer: -1.306

Answer: 0.013

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=0.4, right=2.45; current interior values are [-1.4, -1.0, -1.5]. Use r=0.34. Return the next interior vector.

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


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 855 mL to 0.855 L.
3. Compute M = 4.975 / 0.855.
Final: {"answer": 5.8187, "unit": "mol/L"}

Answer: 5.8187

Prompt: A solution contains 4.975 mol of solute in 855 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 855 mL to 0.855 L.
Compute M = 4.975 / 0.855.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.7)=-11.65 and f(9.2)=-41.4.
3. The interval width is 8.5.
Final: {"answer": -225.4625, "unit": "area_units"}

Answer: -225.4625

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+-9.2 from x=0.7 to x=9.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.7)=-11.65 and f(9.2)=-41.4.
The interval width is 8.5.


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=0.2 and add it to the current value.
Final: {"answer": [2.56, 1.14, -0.28], "unit": "temperature_units"}

Answer: 2.56

Answer: 1.14

Answer: -0.28

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=2.8, right=2.7; current interior values are [2.8, 1.6, -1.9]. Use r=0.2. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.2 and add it to the current value.


Response:
Reasoning:
1. 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_007828(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007828"}

Answer: python_code

Prompt: Write a Python function running_total_007828(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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=81 degrees through the sine of 2 theta.
3. Substitute v=43.3 m/s and g=9.81 m/s^2.
Final: {"answer": 59.0594, "unit": "m"}

Answer: 59.0594

Prompt: A projectile is launched on level ground with no air resistance at speed 43.3 m/s and angle 81 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=81 degrees through the sine of 2 theta.
Substitute v=43.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.5525, "unit": "state_units"}

Answer: 0.5525

Prompt: Use explicit Euler on dy/dt = -0.96 y with y(0)=51, step size h=0.45, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
Apply that update for 8 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=0.28 and add it to the current value.
Final: {"answer": [0.444, 0.448, 1.206], "unit": "temperature_units"}

Answer: 0.444

Answer: 0.448

Answer: 1.206

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=0.4, right=2.65; current interior values are [1.2, -0.7, 1.5]. Use r=0.28. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 834.0 / 100.
Final: {"answer": 8.34, "unit": "m"}

Answer: 8.34

Prompt: Convert 834 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 834.0 / 100.


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 = 4.47 * 8.314 * 572 / 100.5.
Final: {"answer": 211.5181, "unit": "kPa"}

Answer: 211.5181

Prompt: An ideal gas sample has n=4.47 mol, T=572 K, and V=100.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.47 * 8.314 * 572 / 100.5.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=54 mg, t=161.5 h, and T_half=32 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.6336, "unit": "mg"}

Answer: 1.6336

Prompt: A radioactive sample starts with 54 mg. Its half-life is 32 hours. How many mg remain after 161.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=54 mg, t=161.5 h, and T_half=32 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3144.5 / 100.
Final: {"answer": 31.445, "unit": "m"}

Answer: 31.445

Prompt: Convert 3144.5 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 3144.5 / 100.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 10.4^2 and multiply by 0.5 * 22.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1219.504, "unit": "J"}

Answer: 1219.504

Prompt: A body of mass 22.55 kg moves at 10.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.4^2 and multiply by 0.5 * 22.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.9417, "unit": "state_units"}

Answer: 0.9417

Prompt: Use explicit Euler on dy/dt = -0.37 y with y(0)=21.5, step size h=1.75, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [3.0, -19.75], "unit": "dimensionless"}

Answer: 3.0

Answer: -19.75

Prompt: A line passes through points (-14.25, -62.5) and (-9.5, -48.25). 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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=123 mg, t=16.5 h, and T_half=117 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 111.5455, "unit": "mg"}

Answer: 111.5455

Prompt: A radioactive sample starts with 123 mg. Its half-life is 117 hours. How many mg remain after 16.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=123 mg, t=16.5 h, and T_half=117 h.
The remaining amount has the same mass unit as the initial amount.


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=43 V and R=177.9 ohm.
Final: {"answer": 10.3935, "unit": "W"}

Answer: 10.3935

Prompt: A resistor has resistance 177.9 ohm and voltage 43 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=43 V and R=177.9 ohm.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.0, -21.75], "unit": "dimensionless"}

Answer: 7.0

Answer: -21.75

Prompt: A line passes through points (20, 118.25) and (33, 209.25). 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid warehouse experiment records in release 425826, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 90 * 4.675 * 44.
Final: {"answer": 18513.0, "unit": "J"}

Answer: 18513.0

Prompt: A 90 g sample has specific heat 4.675 J/(g*K). How much heat is needed to raise its temperature by 44 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 90 * 4.675 * 44.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=146 mg, t=81.5 h, and T_half=10 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.514, "unit": "mg"}

Answer: 0.514

Prompt: A radioactive sample starts with 146 mg. Its half-life is 10 hours. How many mg remain after 81.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=146 mg, t=81.5 h, and T_half=10 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 14.1342, "unit": "state_units"}

Answer: 14.1342

Prompt: Use explicit Euler on dy/dt = -0.04 y with y(0)=17.5, step size h=1.3, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.5 kg and a = 11.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 87.75, "unit": "N"}

Answer: 87.75

Prompt: A cart has mass 7.5 kg and measured acceleration 11.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.5 kg and a = 11.7 m/s^2.
The unit kg*m/s^2 is one newton.