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_003346(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003346"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003346(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_003346([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003346([], 5) == []

assert threshold_flags_003346([-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: 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)=49.5 and h=0.95, 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 = 22.8 kg and a = 12 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 273.6, "unit": "N"}

Answer: 273.6

Prompt: A cart has mass 22.8 kg and measured acceleration 12 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 = 22.8 kg and a = 12 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 = 6.7^2 and multiply by 0.5 * 23.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 529.702, "unit": "J"}

Answer: 529.702

Prompt: A body of mass 23.6 kg moves at 6.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.7^2 and multiply by 0.5 * 23.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=76 degrees through the sine of 2 theta.
3. Substitute v=70 m/s and g=9.81 m/s^2.
Final: {"answer": 234.4965, "unit": "m"}

Answer: 234.4965

Prompt: A projectile is launched on level ground with no air resistance at speed 70 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=76 degrees through the sine of 2 theta.
Substitute v=70 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.51 * 8.314 * 506 / 56.4.
Final: {"answer": 336.4015, "unit": "kPa"}

Answer: 336.4015

Prompt: An ideal gas sample has n=4.51 mol, T=506 K, and V=56.4 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 = 4.51 * 8.314 * 506 / 56.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1255 * 1.435 * 6.
Final: {"answer": 10805.55, "unit": "J"}

Answer: 10805.55

Prompt: A 1255 g sample has specific heat 1.435 J/(g*K). How much heat is needed to raise its temperature by 6 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1255 * 1.435 * 6.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=204 V and R=89.9 ohm.
Final: {"answer": 462.9143, "unit": "W"}

Answer: 462.9143

Prompt: A resistor has resistance 89.9 ohm and voltage 204 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=204 V and R=89.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=379.5 mg, t=1.5 h, and T_half=116 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 376.1137, "unit": "mg"}

Answer: 376.1137

Prompt: A radioactive sample starts with 379.5 mg. Its half-life is 116 hours. How many mg remain after 1.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=379.5 mg, t=1.5 h, and T_half=116 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.04 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 221.8104, "unit": "g"}

Answer: 221.8104

Prompt: A sample contains 5.04 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.04 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 3585 mL to 3.585 L.
3. Compute M = 0.225 / 3.585.
Final: {"answer": 0.0628, "unit": "mol/L"}

Answer: 0.0628

Prompt: A solution contains 0.225 mol of solute in 3585 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3585 mL to 3.585 L.
Compute M = 0.225 / 3.585.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.7 y with y(0)=56, step size h=1.45, 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) = -0.7 y, so each step multiplies y by 1 - h*0.7.
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(-7.3)=5.61 and f(-1)=-5.1.
3. The interval width is 6.3.
Final: {"answer": 1.6065, "unit": "area_units"}

Answer: 1.6065

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.7x+-6.8 from x=-7.3 to x=-1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.3)=5.61 and f(-1)=-5.1.
The interval width is 6.3.

(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=0.12 and add it to the current value.
Final: {"answer": [2.114, 2.012, 1.728], "unit": "temperature_units"}

Answer: 2.114

Answer: 2.012

Answer: 1.728

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=1.95; current interior values are [2.45, 2.0, 1.65]. Use r=0.12. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 246.0 + 273.15.
Final: {"answer": 519.15, "unit": "K"}

Answer: 519.15

Prompt: Convert 246 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 246.0 + 273.15.


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": [-0.85, -15.25], "unit": "dimensionless"}

Answer: -0.85

Answer: -15.25

Prompt: A line passes through points (2.25, -17.1625) and (12.75, -26.0875). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 620284, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def running_total_003364(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_003364"}

Answer: python_code

Prompt: Write a Python function running_total_003364(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=3.75 mol and T=527 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 = 15.9 kg and a = 5.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 86.655, "unit": "N"}

Answer: 86.655

Prompt: A cart has mass 15.9 kg and measured acceleration 5.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 15.9 kg and a = 5.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.45^2 and multiply by 0.5 * 6.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6.6754, "unit": "J"}

Answer: 6.6754

Prompt: A body of mass 6.35 kg moves at 1.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.45^2 and multiply by 0.5 * 6.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.74 * 8.314 * 508 / 119.5.
Final: {"answer": 26.154, "unit": "kPa"}

Answer: 26.154

Prompt: An ideal gas sample has n=0.74 mol, T=508 K, and V=119.5 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 = 0.74 * 8.314 * 508 / 119.5.


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=71.6 V and R=142 ohm.
Final: {"answer": 36.1025, "unit": "W"}

Answer: 36.1025

Prompt: A resistor has resistance 142 ohm and voltage 71.6 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=71.6 V and R=142 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=117 mg, t=51.5 h, and T_half=2 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 117 mg. Its half-life is 2 hours. How many mg remain after 51.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=117 mg, t=51.5 h, and T_half=2 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 = 4.26 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 76.7439, "unit": "g"}

Answer: 76.7439

Prompt: A sample contains 4.26 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.26 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.9)=31.19 and f(14.2)=83.02.
3. The interval width is 7.3.
Final: {"answer": 416.8665, "unit": "area_units"}

Answer: 416.8665

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+-17.8 from x=6.9 to x=14.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.9)=31.19 and f(14.2)=83.02.
The interval width is 7.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [-0.669, 1.729, 0.709], "unit": "temperature_units"}

Answer: -0.669

Answer: 1.729

Answer: 0.709

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=-0.85, right=2.45; current interior values are [2.85, -1.1, 1.1]. Use r=0.46. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 482.0 / 100.
Final: {"answer": 4.82, "unit": "m"}

Answer: 4.82

Prompt: Convert 482 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 482.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=156 degrees and keep the unit as newtons.
Final: {"answer": [-335.728, 149.4757], "unit": "N"}

Answer: -335.728

Answer: 149.4757

Prompt: A vector has magnitude 367.5 N at 156 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=156 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": [-7.35, 8.75], "unit": "dimensionless"}

Answer: -7.35

Answer: 8.75

Prompt: A line passes through points (15, -101.5) and (29.5, -208.075). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In field worksheet case 461347, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def clamp_003382(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003382"}

Answer: python_code

Prompt: Write a Python function clamp_003382(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_003382(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 30.7 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 = 9.3 kg and a = 11.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 109.275, "unit": "N"}

Answer: 109.275

Prompt: A cart has mass 9.3 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 = 9.3 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 = 31.6^2 and multiply by 0.5 * 7.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3744.6, "unit": "J"}

Answer: 3744.6

Prompt: A body of mass 7.5 kg moves at 31.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.6^2 and multiply by 0.5 * 7.5.
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=29 degrees through the sine of 2 theta.
3. Substitute v=34.1 m/s and g=9.81 m/s^2.
Final: {"answer": 100.5218, "unit": "m"}

Answer: 100.5218

Prompt: A projectile is launched on level ground with no air resistance at speed 34.1 m/s and angle 29 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=29 degrees through the sine of 2 theta.
Substitute v=34.1 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 = 2.15 * 8.314 * 526 / 110.0.
Final: {"answer": 85.4755, "unit": "kPa"}

Answer: 85.4755

Prompt: An ideal gas sample has n=2.15 mol, T=526 K, and V=110.0 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 = 2.15 * 8.314 * 526 / 110.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 360 * 2.365 * 79.
Final: {"answer": 67260.6, "unit": "J"}

Answer: 67260.6

Prompt: A 360 g sample has specific heat 2.365 J/(g*K). How much heat is needed to raise its temperature by 79 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 360 * 2.365 * 79.


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=175.2 V and R=131.1 ohm.
Final: {"answer": 234.1346, "unit": "W"}

Answer: 234.1346

Prompt: A resistor has resistance 131.1 ohm and voltage 175.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=175.2 V and R=131.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=470 mg, t=92.5 h, and T_half=31 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 59.4105, "unit": "mg"}

Answer: 59.4105

Prompt: A radioactive sample starts with 470 mg. Its half-life is 31 hours. How many mg remain after 92.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=470 mg, t=92.5 h, and T_half=31 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 = 2.99 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 131.5899, "unit": "g"}

Answer: 131.5899

Prompt: A sample contains 2.99 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 = 2.99 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 2590 mL to 2.59 L.
3. Compute M = 1.915 / 2.59.
Final: {"answer": 0.7394, "unit": "mol/L"}

Answer: 0.7394

Prompt: A solution contains 1.915 mol of solute in 2590 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2590 mL to 2.59 L.
Compute M = 1.915 / 2.59.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 6.5448, "unit": "state_units"}

Answer: 6.5448

Prompt: Use explicit Euler on dy/dt = -0.8 y with y(0)=50.5, step size h=1.7, 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) = -0.8 y, so each step multiplies y by 1 - h*0.8.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.02 and add it to the current value.
Final: {"answer": [-1.642, 2.233, 0.659], "unit": "temperature_units"}

Answer: -1.642

Answer: 2.233

Answer: 0.659

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=-0.6; current interior values are [-1.8, 2.35, 0.65]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 38.5 + 273.15.
Final: {"answer": 311.65, "unit": "K"}

Answer: 311.65

Prompt: Convert 38.5 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 38.5 + 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=251 degrees and keep the unit as newtons.
Final: {"answer": [-109.3909, -317.6942], "unit": "N"}

Answer: -109.3909

Answer: -317.6942

Prompt: A vector has magnitude 336 N at 251 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=251 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": [-2.5, -9.25], "unit": "dimensionless"}

Answer: -2.5

Answer: -9.25

Prompt: A line passes through points (10.75, -36.125) and (24.75, -71.125). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def safe_mean_003400(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_003400"}

Answer: python_code

Prompt: Write a Python function safe_mean_003400(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_003400([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 13 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=26 degrees through the sine of 2 theta.
3. Substitute v=59.3 m/s and g=9.81 m/s^2.
Final: {"answer": 282.4701, "unit": "m"}

Answer: 282.4701

Prompt: A projectile is launched on level ground with no air resistance at speed 59.3 m/s and angle 26 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=26 degrees through the sine of 2 theta.
Substitute v=59.3 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 = 1815 * 3.125 * 44.
Final: {"answer": 249562.5, "unit": "J"}

Answer: 249562.5

Prompt: A 1815 g sample has specific heat 3.125 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 = 1815 * 3.125 * 44.


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=10.9 V and R=41 ohm.
Final: {"answer": 2.8978, "unit": "W"}

Answer: 2.8978

Prompt: A resistor has resistance 41 ohm and voltage 10.9 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=10.9 V and R=41 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=946 mg, t=319 h, and T_half=119.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 148.6979, "unit": "mg"}

Answer: 148.6979

Prompt: A radioactive sample starts with 946 mg. Its half-life is 119.5 hours. How many mg remain after 319 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=946 mg, t=319 h, and T_half=119.5 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 = 6.34 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 370.5096, "unit": "g"}

Answer: 370.5096

Prompt: A sample contains 6.34 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 = 6.34 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 310 mL to 0.31 L.
3. Compute M = 2.71 / 0.31.
Final: {"answer": 8.7419, "unit": "mol/L"}

Answer: 8.7419

Prompt: A solution contains 2.71 mol of solute in 310 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 310 mL to 0.31 L.
Compute M = 2.71 / 0.31.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0003, "unit": "state_units"}

Answer: 0.0003

Prompt: Use explicit Euler on dy/dt = -0.36 y with y(0)=50.5, step size h=1.95, 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) = -0.36 y, so each step multiplies y by 1 - h*0.36.
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=0.3 and add it to the current value.
Final: {"answer": [-0.26, -0.23, 0.055], "unit": "temperature_units"}

Answer: -0.26

Answer: -0.23

Answer: 0.055

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=1.15, right=-0.6; current interior values are [-0.8, -0.95, 1.3]. Use r=0.3. 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=0.3 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 45026.0 / 1000.
Final: {"answer": 45.026, "unit": "kg"}

Answer: 45.026

Prompt: Convert 45026 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 45026.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=228 degrees and keep the unit as newtons.
Final: {"answer": [-81.6339, -90.6637], "unit": "N"}

Answer: -81.6339

Answer: -90.6637

Prompt: A vector has magnitude 122 N at 228 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=228 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": [-5.4, 6.75], "unit": "dimensionless"}

Answer: -5.4

Answer: 6.75

Prompt: A line passes through points (-15.5, 90.45) and (-12.25, 72.9). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In quality-control check case 160666, 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 pairwise_ratios_003418(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_003418"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_003418(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_003418([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_003418([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 3832 items and budget 8000, 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 = 4.15 kg and a = 4.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 17.845, "unit": "N"}

Answer: 17.845

Prompt: A cart has mass 4.15 kg and measured acceleration 4.3 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 = 4.15 kg and a = 4.3 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 = 42.15^2 and multiply by 0.5 * 25.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 22829.5991, "unit": "J"}

Answer: 22829.5991

Prompt: A body of mass 25.7 kg moves at 42.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.15^2 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=44 degrees through the sine of 2 theta.
3. Substitute v=70.9 m/s and g=9.81 m/s^2.
Final: {"answer": 512.1048, "unit": "m"}

Answer: 512.1048

Prompt: A projectile is launched on level ground with no air resistance at speed 70.9 m/s and angle 44 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=44 degrees through the sine of 2 theta.
Substitute v=70.9 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 = 1980 * 3.51 * 33.
Final: {"answer": 229343.4, "unit": "J"}

Answer: 229343.4

Prompt: A 1980 g sample has specific heat 3.51 J/(g*K). How much heat is needed to raise its temperature by 33 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1980 * 3.51 * 33.


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=133.5 V and R=3.8 ohm.
Final: {"answer": 4690.0658, "unit": "W"}

Answer: 4690.0658

Prompt: A resistor has resistance 3.8 ohm and voltage 133.5 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=133.5 V and R=3.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=292 mg, t=61.5 h, and T_half=87 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 178.8899, "unit": "mg"}

Answer: 178.8899

Prompt: A radioactive sample starts with 292 mg. Its half-life is 87 hours. How many mg remain after 61.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=292 mg, t=61.5 h, and T_half=87 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 = 4.98 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 498.4333, "unit": "g"}

Answer: 498.4333

Prompt: A sample contains 4.98 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 = 4.98 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 60.2783, "unit": "state_units"}

Answer: 60.2783

Prompt: Use explicit Euler on dy/dt = -0.05 y with y(0)=66, step size h=0.3, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.7)=40.44 and f(18.4)=85.68.
3. The interval width is 8.7.
Final: {"answer": 548.622, "unit": "area_units"}

Answer: 548.622

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.2x+-10 from x=9.7 to x=18.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.7)=40.44 and f(18.4)=85.68.
The interval width is 8.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.14 and add it to the current value.
Final: {"answer": [0.316, 2.287, 2.47], "unit": "temperature_units"}

Answer: 0.316

Answer: 2.287

Answer: 2.47

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.7, right=2.6; current interior values are [0.05, 2.7, 2.4]. Use r=0.14. 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=0.14 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 3410.5 / 100.
Final: {"answer": 34.105, "unit": "m"}

Answer: 34.105

Prompt: Convert 3410.5 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 3410.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=156 degrees and keep the unit as newtons.
Final: {"answer": [-309.2351, 137.6804], "unit": "N"}

Answer: -309.2351

Answer: 137.6804

Prompt: A vector has magnitude 338.5 N at 156 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=156 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": [7.9, -17.5], "unit": "dimensionless"}

Answer: 7.9

Answer: -17.5

Prompt: A line passes through points (3.5, 10.15) and (13.25, 87.175). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In simulation spec case 921558, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def center_values_003436(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_003436"}

Answer: python_code

Prompt: Write a Python function center_values_003436(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_003436([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing clinical records in release 303562, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.95 kg and a = 5.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 21.9225, "unit": "N"}

Answer: 21.9225

Prompt: A cart has mass 3.95 kg and measured acceleration 5.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.95 kg and a = 5.55 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 = 41.1^2 and multiply by 0.5 * 4.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3420.6503, "unit": "J"}

Answer: 3420.6503

Prompt: A body of mass 4.05 kg moves at 41.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41.1^2 and multiply by 0.5 * 4.05.
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=24 degrees through the sine of 2 theta.
3. Substitute v=5.5 m/s and g=9.81 m/s^2.
Final: {"answer": 2.2916, "unit": "m"}

Answer: 2.2916

Prompt: A projectile is launched on level ground with no air resistance at speed 5.5 m/s and angle 24 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=24 degrees through the sine of 2 theta.
Substitute v=5.5 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 = 0.46 * 8.314 * 396 / 9.1.
Final: {"answer": 166.4262, "unit": "kPa"}

Answer: 166.4262

Prompt: An ideal gas sample has n=0.46 mol, T=396 K, and V=9.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.46 * 8.314 * 396 / 9.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1925 * 4.925 * 80.
Final: {"answer": 758450.0, "unit": "J"}

Answer: 758450.0

Prompt: A 1925 g sample has specific heat 4.925 J/(g*K). How much heat is needed to raise its temperature by 80 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1925 * 4.925 * 80.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=152.3 V and R=97.2 ohm.
Final: {"answer": 238.6347, "unit": "W"}

Answer: 238.6347

Prompt: A resistor has resistance 97.2 ohm and voltage 152.3 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=152.3 V and R=97.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=322.5 mg, t=228.5 h, and T_half=55.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 18.5846, "unit": "mg"}

Answer: 18.5846

Prompt: A radioactive sample starts with 322.5 mg. Its half-life is 55.5 hours. How many mg remain after 228.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=322.5 mg, t=228.5 h, and T_half=55.5 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 1960 mL to 1.96 L.
3. Compute M = 1.875 / 1.96.
Final: {"answer": 0.9566, "unit": "mol/L"}

Answer: 0.9566

Prompt: A solution contains 1.875 mol of solute in 1960 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1960 mL to 1.96 L.
Compute M = 1.875 / 1.96.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 3.2476, "unit": "state_units"}

Answer: 3.2476

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=22, step size h=1.15, 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) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.6)=30.6 and f(12.8)=56.6.
3. The interval width is 5.2.
Final: {"answer": 226.72, "unit": "area_units"}

Answer: 226.72

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+-7.4 from x=7.6 to x=12.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.6)=30.6 and f(12.8)=56.6.
The interval width is 5.2.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=274 degrees and keep the unit as newtons.
Final: {"answer": [24.6938, -353.1377], "unit": "N"}

Answer: 24.6938

Answer: -353.1377

Prompt: A vector has magnitude 354 N at 274 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=274 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.95, -2.0], "unit": "dimensionless"}

Answer: -5.95

Answer: -2.0

Prompt: A line passes through points (-19, 111.05) and (-15.5, 90.225). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In field worksheet case 764834, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def safe_mean_003454(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_003454"}

Answer: python_code

Prompt: Write a Python function safe_mean_003454(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_003454([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.3 and interior values [-1.65, 1.5, 1.2], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 36.9^2 and multiply by 0.5 * 28.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 19334.862, "unit": "J"}

Answer: 19334.862

Prompt: A body of mass 28.4 kg moves at 36.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 36.9^2 and multiply by 0.5 * 28.4.
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=54 degrees through the sine of 2 theta.
3. Substitute v=78.6 m/s and g=9.81 m/s^2.
Final: {"answer": 598.9387, "unit": "m"}

Answer: 598.9387

Prompt: A projectile is launched on level ground with no air resistance at speed 78.6 m/s and angle 54 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=54 degrees through the sine of 2 theta.
Substitute v=78.6 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 = 4.37 * 8.314 * 447 / 27.6.
Final: {"answer": 588.4233, "unit": "kPa"}

Answer: 588.4233

Prompt: An ideal gas sample has n=4.37 mol, T=447 K, and V=27.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.37 * 8.314 * 447 / 27.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 835 * 2.875 * 113.
Final: {"answer": 271270.625, "unit": "J"}

Answer: 271270.625

Prompt: A 835 g sample has specific heat 2.875 J/(g*K). How much heat is needed to raise its temperature by 113 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 835 * 2.875 * 113.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=631.5 mg, t=162.5 h, and T_half=86 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 170.4381, "unit": "mg"}

Answer: 170.4381

Prompt: A radioactive sample starts with 631.5 mg. Its half-life is 86 hours. How many mg remain after 162.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=631.5 mg, t=162.5 h, and T_half=86 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 = 3.77 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 377.328, "unit": "g"}

Answer: 377.328

Prompt: A sample contains 3.77 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 = 3.77 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 1680 mL to 1.68 L.
3. Compute M = 3.445 / 1.68.
Final: {"answer": 2.0506, "unit": "mol/L"}

Answer: 2.0506

Prompt: A solution contains 3.445 mol of solute in 1680 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1680 mL to 1.68 L.
Compute M = 3.445 / 1.68.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0011, "unit": "state_units"}

Answer: 0.0011

Prompt: Use explicit Euler on dy/dt = -0.43 y with y(0)=5.5, step size h=1.25, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
Apply that update for 11 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=0.06 and add it to the current value.
Final: {"answer": [1.801, -1.55, 1.237], "unit": "temperature_units"}

Answer: 1.801

Answer: -1.55

Answer: 1.237

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=1.35; current interior values are [2.05, -2.0, 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=35 degrees and keep the unit as newtons.
Final: {"answer": [208.0646, 145.6884], "unit": "N"}

Answer: 208.0646

Answer: 145.6884

Prompt: A vector has magnitude 254 N at 35 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=35 degrees and keep the unit as newtons.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid registry invoice records in release 993551, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.4 kg and a = 5.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 90.09, "unit": "N"}

Answer: 90.09

Prompt: A cart has mass 15.4 kg and measured acceleration 5.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 15.4 kg and a = 5.85 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 = 1.95^2 and multiply by 0.5 * 12.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 24.5261, "unit": "J"}

Answer: 24.5261

Prompt: A body of mass 12.9 kg moves at 1.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.95^2 and multiply by 0.5 * 12.9.
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=69 degrees through the sine of 2 theta.
3. Substitute v=30.5 m/s and g=9.81 m/s^2.
Final: {"answer": 63.4515, "unit": "m"}

Answer: 63.4515

Prompt: A projectile is launched on level ground with no air resistance at speed 30.5 m/s and angle 69 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=69 degrees through the sine of 2 theta.
Substitute v=30.5 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 = 3.71 * 8.314 * 507 / 22.9.
Final: {"answer": 682.8989, "unit": "kPa"}

Answer: 682.8989

Prompt: An ideal gas sample has n=3.71 mol, T=507 K, and V=22.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.71 * 8.314 * 507 / 22.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 755 * 4.66 * 4.
Final: {"answer": 14073.2, "unit": "J"}

Answer: 14073.2

Prompt: A 755 g sample has specific heat 4.66 J/(g*K). How much heat is needed to raise its temperature by 4 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 755 * 4.66 * 4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=220.4 V and R=74.5 ohm.
Final: {"answer": 652.029, "unit": "W"}

Answer: 652.029

Prompt: A resistor has resistance 74.5 ohm and voltage 220.4 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=220.4 V and R=74.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.22 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 3.9633, "unit": "g"}

Answer: 3.9633

Prompt: A sample contains 0.22 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.22 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.9)=-19.12 and f(15.5)=-40.4.
3. The interval width is 5.6.
Final: {"answer": -166.656, "unit": "area_units"}

Answer: -166.656

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.8x+18.5 from x=9.9 to x=15.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.9)=-19.12 and f(15.5)=-40.4.
The interval width is 5.6.


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=0.42 and add it to the current value.
Final: {"answer": [0.76, 0.366, -0.815], "unit": "temperature_units"}

Answer: 0.76

Answer: 0.366

Answer: -0.815

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=2.6, right=-1.95; current interior values are [-0.5, -0.6, 1.6]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3408.0 / 100.
Final: {"answer": 34.08, "unit": "m"}

Answer: 34.08

Prompt: Convert 3408 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 3408.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=12 degrees and keep the unit as newtons.
Final: {"answer": [211.769, 45.0129], "unit": "N"}

Answer: 211.769

Answer: 45.0129

Prompt: A vector has magnitude 216.5 N at 12 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=12 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": [5.25, 18.25], "unit": "dimensionless"}

Answer: 5.25

Answer: 18.25

Prompt: A line passes through points (-3, 2.5) and (2.75, 32.6875). 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_003490(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003490"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003490(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_003490([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003490([], 5) == []

assert threshold_flags_003490([-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: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.16 and interior values [0.7, 0.65, 2.8], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.1 kg and a = 15.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 17.545, "unit": "N"}

Answer: 17.545

Prompt: A cart has mass 1.1 kg and measured acceleration 15.95 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 = 1.1 kg and a = 15.95 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=45 degrees through the sine of 2 theta.
3. Substitute v=78.7 m/s and g=9.81 m/s^2.
Final: {"answer": 631.3649, "unit": "m"}

Answer: 631.3649

Prompt: A projectile is launched on level ground with no air resistance at speed 78.7 m/s and angle 45 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=45 degrees through the sine of 2 theta.
Substitute v=78.7 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 = 2.81 * 8.314 * 497 / 47.3.
Final: {"answer": 245.4774, "unit": "kPa"}

Answer: 245.4774

Prompt: An ideal gas sample has n=2.81 mol, T=497 K, and V=47.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.81 * 8.314 * 497 / 47.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 240 * 4.335 * 98.
Final: {"answer": 101959.2, "unit": "J"}

Answer: 101959.2

Prompt: A 240 g sample has specific heat 4.335 J/(g*K). How much heat is needed to raise its temperature by 98 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 240 * 4.335 * 98.


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=188 V and R=2.5 ohm.
Final: {"answer": 14137.6, "unit": "W"}

Answer: 14137.6

Prompt: A resistor has resistance 2.5 ohm and voltage 188 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=188 V and R=2.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=148.5 mg, t=289.5 h, and T_half=41 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.1121, "unit": "mg"}

Answer: 1.1121

Prompt: A radioactive sample starts with 148.5 mg. Its half-life is 41 hours. How many mg remain after 289.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=148.5 mg, t=289.5 h, and T_half=41 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 = 4.77 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 859.3441, "unit": "g"}

Answer: 859.3441

Prompt: A sample contains 4.77 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 = 4.77 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 2500 mL to 2.5 L.
3. Compute M = 4.54 / 2.5.
Final: {"answer": 1.816, "unit": "mol/L"}

Answer: 1.816

Prompt: A solution contains 4.54 mol of solute in 2500 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2500 mL to 2.5 L.
Compute M = 4.54 / 2.5.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(10)=11.6 and f(20)=34.6.
3. The interval width is 10.
Final: {"answer": 231.0, "unit": "area_units"}

Answer: 231.0

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.3x+-11.4 from x=10 to x=20. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(10)=11.6 and f(20)=34.6.
The interval width is 10.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -47.5 + 273.15.
Final: {"answer": 225.65, "unit": "K"}

Answer: 225.65

Prompt: Convert -47.5 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 -47.5 + 273.15.


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": [-2.9, -3.75], "unit": "dimensionless"}

Answer: -2.9

Answer: -3.75

Prompt: A line passes through points (-6.5, 15.1) and (-2.25, 2.775). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. energy divided by length is force, not spring constant
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In student derivation case 299417, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
energy divided by length is force, not spring constant
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def running_total_003508(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_003508"}

Answer: python_code

Prompt: Write a Python function running_total_003508(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: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.26 and interior values [1.7, -1.5, -0.1], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.2^2 and multiply by 0.5 * 17.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 12.672, "unit": "J"}

Answer: 12.672

Prompt: A body of mass 17.6 kg moves at 1.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.2^2 and multiply by 0.5 * 17.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=81 degrees through the sine of 2 theta.
3. Substitute v=60.9 m/s and g=9.81 m/s^2.
Final: {"answer": 116.8283, "unit": "m"}

Answer: 116.8283

Prompt: A projectile is launched on level ground with no air resistance at speed 60.9 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=60.9 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 = 2.94 * 8.314 * 427 / 35.5.
Final: {"answer": 294.0065, "unit": "kPa"}

Answer: 294.0065

Prompt: An ideal gas sample has n=2.94 mol, T=427 K, and V=35.5 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 = 2.94 * 8.314 * 427 / 35.5.


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=169 V and R=43.7 ohm.
Final: {"answer": 653.5698, "unit": "W"}

Answer: 653.5698

Prompt: A resistor has resistance 43.7 ohm and voltage 169 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=169 V and R=43.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=171.5 mg, t=12.5 h, and T_half=96 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 156.6995, "unit": "mg"}

Answer: 156.6995

Prompt: A radioactive sample starts with 171.5 mg. Its half-life is 96 hours. How many mg remain after 12.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=171.5 mg, t=12.5 h, and T_half=96 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) = -1 y, so each step multiplies y by 1 - h*1.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": -0.033, "unit": "state_units"}

Answer: -0.033

Prompt: Use explicit Euler on dy/dt = -1 y with y(0)=33, step size h=1.1, 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) = -1 y, so each step multiplies y by 1 - h*1.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.5)=-36.05 and f(2.3)=2.17.
3. The interval width is 9.8.
Final: {"answer": -166.012, "unit": "area_units"}

Answer: -166.012

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.9x+-6.8 from x=-7.5 to x=2.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.5)=-36.05 and f(2.3)=2.17.
The interval width is 9.8.


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=0.18 and add it to the current value.
Final: {"answer": [1.536, 1.198, 1.976], "unit": "temperature_units"}

Answer: 1.536

Answer: 1.198

Answer: 1.976

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=2.25; current interior values are [2.4, 0.55, 2.3]. Use r=0.18. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.18 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 47522.0 / 1000.
Final: {"answer": 47.522, "unit": "kg"}

Answer: 47.522

Prompt: Convert 47522 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 47522.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=121 degrees and keep the unit as newtons.
Final: {"answer": [-194.1694, 323.1521], "unit": "N"}

Answer: -194.1694

Answer: 323.1521

Prompt: A vector has magnitude 377 N at 121 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=121 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. energy divided by length is force, not spring constant
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In student derivation case 920586, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
energy divided by length is force, not spring constant
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def threshold_flags_003526(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003526"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003526(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_003526([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003526([], 5) == []

assert threshold_flags_003526([-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 34.7 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 = 2.85 kg and a = 14.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 40.47, "unit": "N"}

Answer: 40.47

Prompt: A cart has mass 2.85 kg and measured acceleration 14.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.85 kg and a = 14.2 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=656 mg, t=142.5 h, and T_half=106 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 258.3552, "unit": "mg"}

Answer: 258.3552

Prompt: A radioactive sample starts with 656 mg. Its half-life is 106 hours. How many mg remain after 142.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=656 mg, t=142.5 h, and T_half=106 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 1540 mL to 1.54 L.
3. Compute M = 4.925 / 1.54.
Final: {"answer": 3.1981, "unit": "mol/L"}

Answer: 3.1981

Prompt: A solution contains 4.925 mol of solute in 1540 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1540 mL to 1.54 L.
Compute M = 4.925 / 1.54.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 20.3426, "unit": "state_units"}

Answer: 20.3426

Prompt: Use explicit Euler on dy/dt = -0.47 y with y(0)=71, step size h=0.25, 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) = -0.47 y, so each step multiplies y by 1 - h*0.47.
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(-7.7)=-49.71 and f(-5.2)=-36.46.
3. The interval width is 2.5.
Final: {"answer": -107.7125, "unit": "area_units"}

Answer: -107.7125

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.3x+-8.9 from x=-7.7 to x=-5.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.7)=-49.71 and f(-5.2)=-36.46.
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=0.2 and add it to the current value.
Final: {"answer": [0.33, 1.1, 0.39], "unit": "temperature_units"}

Answer: 0.33

Answer: 1.1

Answer: 0.39

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=2.9, right=1.7; current interior values are [-1.25, 2.5, -0.75]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -38.5 + 273.15.
Final: {"answer": 234.65, "unit": "K"}

Answer: 234.65

Prompt: Convert -38.5 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 -38.5 + 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=137 degrees and keep the unit as newtons.
Final: {"answer": [-315.5791, 294.2823], "unit": "N"}

Answer: -315.5791

Answer: 294.2823

Prompt: A vector has magnitude 431.5 N at 137 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=137 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.15, 24.25], "unit": "dimensionless"}

Answer: 7.15

Answer: 24.25

Prompt: A line passes through points (-9.25, -41.8875) and (-4.75, -9.7125). 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 447898, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_003544(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_003544"}

Answer: python_code

Prompt: Write a Python function unit_vector_003544(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_003544(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)=11.5 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. Use Newton's second law F = m a.
2. Substitute m = 9.5 kg and a = 13.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 132.525, "unit": "N"}

Answer: 132.525

Prompt: A cart has mass 9.5 kg and measured acceleration 13.95 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 = 9.5 kg and a = 13.95 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 = 31.05^2 and multiply by 0.5 * 9.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4796.4099, "unit": "J"}

Answer: 4796.4099

Prompt: A body of mass 9.95 kg moves at 31.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.05^2 and multiply by 0.5 * 9.95.
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=55 degrees through the sine of 2 theta.
3. Substitute v=26.2 m/s and g=9.81 m/s^2.
Final: {"answer": 65.7536, "unit": "m"}

Answer: 65.7536

Prompt: A projectile is launched on level ground with no air resistance at speed 26.2 m/s and angle 55 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=55 degrees through the sine of 2 theta.
Substitute v=26.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.88 * 8.314 * 497 / 57.3.
Final: {"answer": 207.6846, "unit": "kPa"}

Answer: 207.6846

Prompt: An ideal gas sample has n=2.88 mol, T=497 K, and V=57.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.88 * 8.314 * 497 / 57.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 235 * 1.115 * 51.
Final: {"answer": 13363.275, "unit": "J"}

Answer: 13363.275

Prompt: A 235 g sample has specific heat 1.115 J/(g*K). How much heat is needed to raise its temperature by 51 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 235 * 1.115 * 51.


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=197.6 V and R=3 ohm.
Final: {"answer": 13015.2533, "unit": "W"}

Answer: 13015.2533

Prompt: A resistor has resistance 3 ohm and voltage 197.6 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=197.6 V and R=3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=124.5 mg, t=225.5 h, and T_half=11 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0001, "unit": "mg"}

Answer: 0.0001

Prompt: A radioactive sample starts with 124.5 mg. Its half-life is 11 hours. How many mg remain after 225.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=124.5 mg, t=225.5 h, and T_half=11 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 = 0.37 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 16.2837, "unit": "g"}

Answer: 16.2837

Prompt: A sample contains 0.37 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 = 0.37 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 12.0262, "unit": "state_units"}

Answer: 12.0262

Prompt: Use explicit Euler on dy/dt = -0.12 y with y(0)=38, step size h=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) = -0.12 y, so each step multiplies y by 1 - h*0.12.
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(-1.4)=7.42 and f(-0.5)=13.45.
3. The interval width is 0.9.
Final: {"answer": 9.3915, "unit": "area_units"}

Answer: 9.3915

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+16.8 from x=-1.4 to x=-0.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.4)=7.42 and f(-0.5)=13.45.
The interval width is 0.9.


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=0.46 and add it to the current value.
Final: {"answer": [2.083, 0.245, 0.091], "unit": "temperature_units"}

Answer: 2.083

Answer: 0.245

Answer: 0.091

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=2.05, right=-1.75; current interior values are [1.6, 2.2, -1.45]. Use r=0.46. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 9145.0 / 1000.
Final: {"answer": 9.145, "unit": "kg"}

Answer: 9.145

Prompt: Convert 9145 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 9145.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=267 degrees and keep the unit as newtons.
Final: {"answer": [-4.9457, -94.3705], "unit": "N"}

Answer: -4.9457

Answer: -94.3705

Prompt: A vector has magnitude 94.5 N at 267 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=267 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": [-5.8, -3.5], "unit": "dimensionless"}

Answer: -5.8

Answer: -3.5

Prompt: A line passes through points (-4.75, 24.05) and (0, -3.5). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 200786, 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 pairwise_ratios_003562(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_003562"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_003562(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_003562([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_003562([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass