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 sensor records in release 920031, 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 = 2.9 kg and a = 6.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 18.415, "unit": "N"}

Answer: 18.415

Prompt: A cart has mass 2.9 kg and measured acceleration 6.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.9 kg and a = 6.35 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 = 23.5^2 and multiply by 0.5 * 22.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6281.8438, "unit": "J"}

Answer: 6281.8438

Prompt: A body of mass 22.75 kg moves at 23.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.5^2 and multiply by 0.5 * 22.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=41 degrees through the sine of 2 theta.
3. Substitute v=68.6 m/s and g=9.81 m/s^2.
Final: {"answer": 475.042, "unit": "m"}

Answer: 475.042

Prompt: A projectile is launched on level ground with no air resistance at speed 68.6 m/s and angle 41 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=41 degrees through the sine of 2 theta.
Substitute v=68.6 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.38 * 8.314 * 501 / 66.2.
Final: {"answer": 23.9097, "unit": "kPa"}

Answer: 23.9097

Prompt: An ideal gas sample has n=0.38 mol, T=501 K, and V=66.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.38 * 8.314 * 501 / 66.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1780 * 4.275 * 33.
Final: {"answer": 251113.5, "unit": "J"}

Answer: 251113.5

Prompt: A 1780 g sample has specific heat 4.275 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 = 1780 * 4.275 * 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=171.7 V and R=169 ohm.
Final: {"answer": 174.4431, "unit": "W"}

Answer: 174.4431

Prompt: A resistor has resistance 169 ohm and voltage 171.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=171.7 V and R=169 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=897.5 mg, t=349.5 h, and T_half=55.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 11.4119, "unit": "mg"}

Answer: 11.4119

Prompt: A radioactive sample starts with 897.5 mg. Its half-life is 55.5 hours. How many mg remain after 349.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=897.5 mg, t=349.5 h, and T_half=55.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.94 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 217.4094, "unit": "g"}

Answer: 217.4094

Prompt: A sample contains 4.94 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.94 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 2065 mL to 2.065 L.
3. Compute M = 4.685 / 2.065.
Final: {"answer": 2.2688, "unit": "mol/L"}

Answer: 2.2688

Prompt: A solution contains 4.685 mol of solute in 2065 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2065 mL to 2.065 L.
Compute M = 4.685 / 2.065.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.75 y, so each step multiplies y by 1 - h*0.75.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.75 y with y(0)=78, step size h=1.25, 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) = -0.75 y, so each step multiplies y by 1 - h*0.75.
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(2.1)=-18.19 and f(8.4)=-23.86.
3. The interval width is 6.3.
Final: {"answer": -132.4575, "unit": "area_units"}

Answer: -132.4575

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.9x+-16.3 from x=2.1 to x=8.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.1)=-18.19 and f(8.4)=-23.86.
The interval width is 6.3.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 9507.0 / 1000.
Final: {"answer": 9.507, "unit": "kg"}

Answer: 9.507

Prompt: Convert 9507 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 9507.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=177 degrees and keep the unit as newtons.
Final: {"answer": [-14.4801, 0.7589], "unit": "N"}

Answer: -14.4801

Answer: 0.7589

Prompt: A vector has magnitude 14.5 N at 177 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=177 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [0.2, -8.75], "unit": "dimensionless"}

Answer: 0.2

Answer: -8.75

Prompt: A line passes through points (-8.75, -10.5) and (-8.25, -10.4). 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 finite_differences_002914(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002914"}

Answer: python_code

Prompt: Write a Python function finite_differences_002914(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. 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 finite_differences_002914([5]) == []

assert finite_differences_002914([]) == []


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 clinical records in release 292671, 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 = 17.55 kg and a = 8.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 143.91, "unit": "N"}

Answer: 143.91

Prompt: A cart has mass 17.55 kg and measured acceleration 8.2 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 = 17.55 kg and a = 8.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.54 * 8.314 * 314 / 64.6.
Final: {"answer": 102.6457, "unit": "kPa"}

Answer: 102.6457

Prompt: An ideal gas sample has n=2.54 mol, T=314 K, and V=64.6 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 = 2.54 * 8.314 * 314 / 64.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1135 * 3.06 * 104.
Final: {"answer": 361202.4, "unit": "J"}

Answer: 361202.4

Prompt: A 1135 g sample has specific heat 3.06 J/(g*K). How much heat is needed to raise its temperature by 104 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1135 * 3.06 * 104.


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=215.2 V and R=129.2 ohm.
Final: {"answer": 358.4446, "unit": "W"}

Answer: 358.4446

Prompt: A resistor has resistance 129.2 ohm and voltage 215.2 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=215.2 V and R=129.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=936.5 mg, t=33.5 h, and T_half=24.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 362.9906, "unit": "mg"}

Answer: 362.9906

Prompt: A radioactive sample starts with 936.5 mg. Its half-life is 24.5 hours. How many mg remain after 33.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=936.5 mg, t=33.5 h, and T_half=24.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.97 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 71.5196, "unit": "g"}

Answer: 71.5196

Prompt: A sample contains 3.97 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 = 3.97 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3205 mL to 3.205 L.
3. Compute M = 0.78 / 3.205.
Final: {"answer": 0.2434, "unit": "mol/L"}

Answer: 0.2434

Prompt: A solution contains 0.78 mol of solute in 3205 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3205 mL to 3.205 L.
Compute M = 0.78 / 3.205.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 12.177, "unit": "state_units"}

Answer: 12.177

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=15, step size h=1.1, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.2)=-22 and f(-3.5)=-18.3.
3. The interval width is 3.7.
Final: {"answer": -74.555, "unit": "area_units"}

Answer: -74.555

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1x+-14.8 from x=-7.2 to x=-3.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.2)=-22 and f(-3.5)=-18.3.
The interval width is 3.7.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 128.0 + 273.15.
Final: {"answer": 401.15, "unit": "K"}

Answer: 401.15

Prompt: Convert 128 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 128.0 + 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": [3.9, -23.25], "unit": "dimensionless"}

Answer: 3.9

Answer: -23.25

Prompt: A line passes through points (-5.75, -45.675) and (1.75, -16.425). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 166696, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
grams cancel with J/(g*K), and kelvin cancels, leaving joules
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

```python
def pairwise_ratios_002932(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_002932"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_002932(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_002932([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_002932([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: 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 81.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.05 kg and a = 5.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 30.855, "unit": "N"}

Answer: 30.855

Prompt: A cart has mass 6.05 kg and measured acceleration 5.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.05 kg and a = 5.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.05^2 and multiply by 0.5 * 19.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10.6943, "unit": "J"}

Answer: 10.6943

Prompt: A body of mass 19.4 kg moves at 1.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.05^2 and multiply by 0.5 * 19.4.
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=22 degrees through the sine of 2 theta.
3. Substitute v=78.9 m/s and g=9.81 m/s^2.
Final: {"answer": 440.8149, "unit": "m"}

Answer: 440.8149

Prompt: A projectile is launched on level ground with no air resistance at speed 78.9 m/s and angle 22 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=22 degrees through the sine of 2 theta.
Substitute v=78.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.63 * 8.314 * 616 / 3.2.
Final: {"answer": 2608.7253, "unit": "kPa"}

Answer: 2608.7253

Prompt: An ideal gas sample has n=1.63 mol, T=616 K, and V=3.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.63 * 8.314 * 616 / 3.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 830 * 0.9 * 111.
Final: {"answer": 82917.0, "unit": "J"}

Answer: 82917.0

Prompt: A 830 g sample has specific heat 0.9 J/(g*K). How much heat is needed to raise its temperature by 111 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 830 * 0.9 * 111.


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=129.9 V and R=116.7 ohm.
Final: {"answer": 144.5931, "unit": "W"}

Answer: 144.5931

Prompt: A resistor has resistance 116.7 ohm and voltage 129.9 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=129.9 V and R=116.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=697 mg, t=6 h, and T_half=95 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 667.1452, "unit": "mg"}

Answer: 667.1452

Prompt: A radioactive sample starts with 697 mg. Its half-life is 95 hours. How many mg remain after 6 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=697 mg, t=6 h, and T_half=95 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 = 4.81 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 866.5504, "unit": "g"}

Answer: 866.5504

Prompt: A sample contains 4.81 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 = 4.81 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 185 mL to 0.185 L.
3. Compute M = 1.825 / 0.185.
Final: {"answer": 9.8649, "unit": "mol/L"}

Answer: 9.8649

Prompt: A solution contains 1.825 mol of solute in 185 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 185 mL to 0.185 L.
Compute M = 1.825 / 0.185.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.88 y with y(0)=29, step size h=1.4, 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) = -0.88 y, so each step multiplies y by 1 - h*0.88.
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=0.18 and add it to the current value.
Final: {"answer": [1.474, 2.06, 2.281], "unit": "temperature_units"}

Answer: 1.474

Answer: 2.06

Answer: 2.281

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=1.1; current interior values are [1.15, 2.15, 2.65]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 120.0 + 273.15.
Final: {"answer": 393.15, "unit": "K"}

Answer: 393.15

Prompt: Convert 120 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 120.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=46 degrees and keep the unit as newtons.
Final: {"answer": [254.5923, 263.638], "unit": "N"}

Answer: 254.5923

Answer: 263.638

Prompt: A vector has magnitude 366.5 N at 46 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=46 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": [7.65, -25.25], "unit": "dimensionless"}

Answer: 7.65

Answer: -25.25

Prompt: A line passes through points (-3, -48.2) and (6.5, 24.475). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In model card equation case 169246, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_002950(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_002950"}

Answer: python_code

Prompt: Write a Python function unit_vector_002950(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_002950(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 59.1 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.05 kg and a = 9.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 232.0825, "unit": "N"}

Answer: 232.0825

Prompt: A cart has mass 24.05 kg and measured acceleration 9.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.05 kg and a = 9.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 35.8^2 and multiply by 0.5 * 28.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 18391.534, "unit": "J"}

Answer: 18391.534

Prompt: A body of mass 28.7 kg moves at 35.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 35.8^2 and multiply by 0.5 * 28.7.
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 = 2.04 * 8.314 * 255 / 17.1.
Final: {"answer": 252.9206, "unit": "kPa"}

Answer: 252.9206

Prompt: An ideal gas sample has n=2.04 mol, T=255 K, and V=17.1 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 = 2.04 * 8.314 * 255 / 17.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1120 * 1.975 * 77.
Final: {"answer": 170324.0, "unit": "J"}

Answer: 170324.0

Prompt: A 1120 g sample has specific heat 1.975 J/(g*K). How much heat is needed to raise its temperature by 77 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1120 * 1.975 * 77.


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=117.1 V and R=15.1 ohm.
Final: {"answer": 908.1066, "unit": "W"}

Answer: 908.1066

Prompt: A resistor has resistance 15.1 ohm and voltage 117.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=117.1 V and R=15.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=900.5 mg, t=273 h, and T_half=54.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 27.9622, "unit": "mg"}

Answer: 27.9622

Prompt: A radioactive sample starts with 900.5 mg. Its half-life is 54.5 hours. How many mg remain after 273 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=900.5 mg, t=273 h, and T_half=54.5 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 = 1.2 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 120.1044, "unit": "g"}

Answer: 120.1044

Prompt: A sample contains 1.2 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.2 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 3795 mL to 3.795 L.
3. Compute M = 2.19 / 3.795.
Final: {"answer": 0.5771, "unit": "mol/L"}

Answer: 0.5771

Prompt: A solution contains 2.19 mol of solute in 3795 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3795 mL to 3.795 L.
Compute M = 2.19 / 3.795.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0578, "unit": "state_units"}

Answer: 0.0578

Prompt: Use explicit Euler on dy/dt = -0.64 y with y(0)=22, step size h=0.7, 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) = -0.64 y, so each step multiplies y by 1 - h*0.64.
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(7.4)=34.62 and f(15.4)=73.02.
3. The interval width is 8.
Final: {"answer": 430.56, "unit": "area_units"}

Answer: 430.56

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-0.9 from x=7.4 to x=15.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.4)=34.62 and f(15.4)=73.02.
The interval width is 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=0.36 and add it to the current value.
Final: {"answer": [1.348, -0.128, 1.3], "unit": "temperature_units"}

Answer: 1.348

Answer: -0.128

Answer: 1.3

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=2.65, right=2.75; current interior values are [-0.65, 1.6, -0.95]. Use r=0.36. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2544.5 / 100.
Final: {"answer": 25.445, "unit": "m"}

Answer: 25.445

Prompt: Convert 2544.5 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 2544.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=356 degrees and keep the unit as newtons.
Final: {"answer": [297.2741, -20.7874], "unit": "N"}

Answer: 297.2741

Answer: -20.7874

Prompt: A vector has magnitude 298 N at 356 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=356 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.25, 12.75], "unit": "dimensionless"}

Answer: 4.25

Answer: 12.75

Prompt: A line passes through points (-10, -29.75) and (-1, 8.5). 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. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 654509, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def center_values_002968(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_002968"}

Answer: python_code

Prompt: Write a Python function center_values_002968(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_002968([])
    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 4176 items and budget 56695, 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 = 4.65 kg and a = 1.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 6.045, "unit": "N"}

Answer: 6.045

Prompt: A cart has mass 4.65 kg and measured acceleration 1.3 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 = 4.65 kg and a = 1.3 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 = 41.7^2 and multiply by 0.5 * 3.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2782.224, "unit": "J"}

Answer: 2782.224

Prompt: A body of mass 3.2 kg moves at 41.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41.7^2 and multiply by 0.5 * 3.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=8 degrees through the sine of 2 theta.
3. Substitute v=21.5 m/s and g=9.81 m/s^2.
Final: {"answer": 12.9881, "unit": "m"}

Answer: 12.9881

Prompt: A projectile is launched on level ground with no air resistance at speed 21.5 m/s and angle 8 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=8 degrees through the sine of 2 theta.
Substitute v=21.5 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 = 4.19 * 8.314 * 584 / 83.6.
Final: {"answer": 243.3496, "unit": "kPa"}

Answer: 243.3496

Prompt: An ideal gas sample has n=4.19 mol, T=584 K, and V=83.6 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 = 4.19 * 8.314 * 584 / 83.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1990 * 3.28 * 66.
Final: {"answer": 430795.2, "unit": "J"}

Answer: 430795.2

Prompt: A 1990 g sample has specific heat 3.28 J/(g*K). How much heat is needed to raise its temperature by 66 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1990 * 3.28 * 66.


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=53.5 V and R=182.2 ohm.
Final: {"answer": 15.7094, "unit": "W"}

Answer: 15.7094

Prompt: A resistor has resistance 182.2 ohm and voltage 53.5 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=53.5 V and R=182.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=89 mg, t=358.5 h, and T_half=110.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 9.3917, "unit": "mg"}

Answer: 9.3917

Prompt: A radioactive sample starts with 89 mg. Its half-life is 110.5 hours. How many mg remain after 358.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=89 mg, t=358.5 h, and T_half=110.5 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 = 6.6 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1189.0296, "unit": "g"}

Answer: 1189.0296

Prompt: A sample contains 6.6 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.6 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.6)=3.68 and f(12)=13.3.
3. The interval width is 7.4.
Final: {"answer": 62.826, "unit": "area_units"}

Answer: 62.826

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.3x+-2.3 from x=4.6 to x=12. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.6)=3.68 and f(12)=13.3.
The interval width is 7.4.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3452.5 / 100.
Final: {"answer": 34.525, "unit": "m"}

Answer: 34.525

Prompt: Convert 3452.5 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 3452.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=213 degrees and keep the unit as newtons.
Final: {"answer": [-164.3794, -106.7493], "unit": "N"}

Answer: -164.3794

Answer: -106.7493

Prompt: A vector has magnitude 196 N at 213 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=213 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.0, -16.25], "unit": "dimensionless"}

Answer: 2.0

Answer: -16.25

Prompt: A line passes through points (-12.5, -41.25) and (2.5, -11.25). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def normalize_002986(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_002986"}

Answer: python_code

Prompt: Write a Python function normalize_002986(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_002986([2, 3, 5]); assert len(out) == 3

try:
    normalize_002986([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 1766 items and budget 28575, 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 = 11.55 kg and a = 4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 46.2, "unit": "N"}

Answer: 46.2

Prompt: A cart has mass 11.55 kg and measured acceleration 4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 11.55 kg and a = 4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 41.5^2 and multiply by 0.5 * 5.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5080.6375, "unit": "J"}

Answer: 5080.6375

Prompt: A body of mass 5.9 kg moves at 41.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41.5^2 and multiply by 0.5 * 5.9.
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=16 degrees through the sine of 2 theta.
3. Substitute v=13.9 m/s and g=9.81 m/s^2.
Final: {"answer": 10.4369, "unit": "m"}

Answer: 10.4369

Prompt: A projectile is launched on level ground with no air resistance at speed 13.9 m/s and angle 16 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=16 degrees through the sine of 2 theta.
Substitute v=13.9 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 = 5.71 * 8.314 * 466 / 57.1.
Final: {"answer": 387.4324, "unit": "kPa"}

Answer: 387.4324

Prompt: An ideal gas sample has n=5.71 mol, T=466 K, and V=57.1 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 = 5.71 * 8.314 * 466 / 57.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1965 * 0.79 * 54.
Final: {"answer": 83826.9, "unit": "J"}

Answer: 83826.9

Prompt: A 1965 g sample has specific heat 0.79 J/(g*K). How much heat is needed to raise its temperature by 54 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1965 * 0.79 * 54.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=182.2 V and R=104.9 ohm.
Final: {"answer": 316.4618, "unit": "W"}

Answer: 316.4618

Prompt: A resistor has resistance 104.9 ohm and voltage 182.2 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=182.2 V and R=104.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=80 mg, t=251 h, and T_half=34.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.5164, "unit": "mg"}

Answer: 0.5164

Prompt: A radioactive sample starts with 80 mg. Its half-life is 34.5 hours. How many mg remain after 251 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=80 mg, t=251 h, and T_half=34.5 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 = 6.99 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 699.6081, "unit": "g"}

Answer: 699.6081

Prompt: A sample contains 6.99 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.99 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 4330 mL to 4.33 L.
3. Compute M = 0.35 / 4.33.
Final: {"answer": 0.0808, "unit": "mol/L"}

Answer: 0.0808

Prompt: A solution contains 0.35 mol of solute in 4330 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4330 mL to 4.33 L.
Compute M = 0.35 / 4.33.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 3.3933, "unit": "state_units"}

Answer: 3.3933

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=42, step size h=1.95, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
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(-0.5)=-8.3 and f(3)=-26.5.
3. The interval width is 3.5.
Final: {"answer": -60.9, "unit": "area_units"}

Answer: -60.9

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.2x+-10.9 from x=-0.5 to x=3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.5)=-8.3 and f(3)=-26.5.
The interval width is 3.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.24 and add it to the current value.
Final: {"answer": [-0.458, 0.57, 1.6], "unit": "temperature_units"}

Answer: -0.458

Answer: 0.57

Answer: 1.6

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=2.5; current interior values are [-1.85, 1.35, 1.3]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 27.0 + 273.15.
Final: {"answer": 300.15, "unit": "K"}

Answer: 300.15

Prompt: Convert 27 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 27.0 + 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": [0.3, 23.0], "unit": "dimensionless"}

Answer: 0.3

Answer: 23.0

Prompt: A line passes through points (7.5, 25.25) and (13.75, 27.125). 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. 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 118785, 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 threshold_flags_003004(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003004"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003004(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_003004([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003004([], 5) == []

assert threshold_flags_003004([-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 61.7 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 = 2.8 kg and a = 12.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 35.14, "unit": "N"}

Answer: 35.14

Prompt: A cart has mass 2.8 kg and measured acceleration 12.55 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 = 2.8 kg and a = 12.55 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 = 2.85^2 and multiply by 0.5 * 11.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 48.3289, "unit": "J"}

Answer: 48.3289

Prompt: A body of mass 11.9 kg moves at 2.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.85^2 and multiply by 0.5 * 11.9.
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=82 degrees through the sine of 2 theta.
3. Substitute v=38.3 m/s and g=9.81 m/s^2.
Final: {"answer": 41.2161, "unit": "m"}

Answer: 41.2161

Prompt: A projectile is launched on level ground with no air resistance at speed 38.3 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=82 degrees through the sine of 2 theta.
Substitute v=38.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=40.6 V and R=43 ohm.
Final: {"answer": 38.334, "unit": "W"}

Answer: 38.334

Prompt: A resistor has resistance 43 ohm and voltage 40.6 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=40.6 V and R=43 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=840.5 mg, t=171 h, and T_half=64.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 133.8006, "unit": "mg"}

Answer: 133.8006

Prompt: A radioactive sample starts with 840.5 mg. Its half-life is 64.5 hours. How many mg remain after 171 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=840.5 mg, t=171 h, and T_half=64.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.94 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 173.3994, "unit": "g"}

Answer: 173.3994

Prompt: A sample contains 3.94 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 = 3.94 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 4845 mL to 4.845 L.
3. Compute M = 2.96 / 4.845.
Final: {"answer": 0.6109, "unit": "mol/L"}

Answer: 0.6109

Prompt: A solution contains 2.96 mol of solute in 4845 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4845 mL to 4.845 L.
Compute M = 2.96 / 4.845.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 10.5567, "unit": "state_units"}

Answer: 10.5567

Prompt: Use explicit Euler on dy/dt = -0.13 y with y(0)=15, step size h=0.85, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4.3)=2.87 and f(3)=-32.9.
3. The interval width is 7.3.
Final: {"answer": -109.6095, "unit": "area_units"}

Answer: -109.6095

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-18.2 from x=-4.3 to x=3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.3)=2.87 and f(3)=-32.9.
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=0.08 and add it to the current value.
Final: {"answer": [-1.038, -1.03, -1.65], "unit": "temperature_units"}

Answer: -1.038

Answer: -1.03

Answer: -1.65

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=0.05, right=-1.3; current interior values are [-1.15, -0.95, -1.75]. Use r=0.08. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.08 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 197.5 + 273.15.
Final: {"answer": 470.65, "unit": "K"}

Answer: 470.65

Prompt: Convert 197.5 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 197.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=16 degrees and keep the unit as newtons.
Final: {"answer": [12.977, 3.7211], "unit": "N"}

Answer: 12.977

Answer: 3.7211

Prompt: A vector has magnitude 13.5 N at 16 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=16 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.35, 3.0], "unit": "dimensionless"}

Answer: 4.35

Answer: 3.0

Prompt: A line passes through points (14.75, 67.1625) and (15.5, 70.425). 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 student derivation case 435984, 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 normalize_003022(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_003022"}

Answer: python_code

Prompt: Write a Python function normalize_003022(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_003022([2, 3, 5]); assert len(out) == 3

try:
    normalize_003022([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 49 items and budget 70905, 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 = 4.6 kg and a = 6.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 31.51, "unit": "N"}

Answer: 31.51

Prompt: A cart has mass 4.6 kg and measured acceleration 6.85 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 = 4.6 kg and a = 6.85 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 = 7.85^2 and multiply by 0.5 * 21.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 656.2796, "unit": "J"}

Answer: 656.2796

Prompt: A body of mass 21.3 kg moves at 7.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.85^2 and multiply by 0.5 * 21.3.
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=36 degrees through the sine of 2 theta.
3. Substitute v=31 m/s and g=9.81 m/s^2.
Final: {"answer": 93.1667, "unit": "m"}

Answer: 93.1667

Prompt: A projectile is launched on level ground with no air resistance at speed 31 m/s and angle 36 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=36 degrees through the sine of 2 theta.
Substitute v=31 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 = 0.99 * 8.314 * 456 / 57.8.
Final: {"answer": 64.9355, "unit": "kPa"}

Answer: 64.9355

Prompt: An ideal gas sample has n=0.99 mol, T=456 K, and V=57.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.99 * 8.314 * 456 / 57.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1085 * 2.755 * 116.
Final: {"answer": 346744.3, "unit": "J"}

Answer: 346744.3

Prompt: A 1085 g sample has specific heat 2.755 J/(g*K). How much heat is needed to raise its temperature by 116 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1085 * 2.755 * 116.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=94 mg, t=202 h, and T_half=87 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 18.8012, "unit": "mg"}

Answer: 18.8012

Prompt: A radioactive sample starts with 94 mg. Its half-life is 87 hours. How many mg remain after 202 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=94 mg, t=202 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 = 1.18 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 212.5841, "unit": "g"}

Answer: 212.5841

Prompt: A sample contains 1.18 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.18 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 3455 mL to 3.455 L.
3. Compute M = 4.18 / 3.455.
Final: {"answer": 1.2098, "unit": "mol/L"}

Answer: 1.2098

Prompt: A solution contains 4.18 mol of solute in 3455 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3455 mL to 3.455 L.
Compute M = 4.18 / 3.455.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.8636, "unit": "state_units"}

Answer: 0.8636

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=13, step size h=0.7, 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) = -0.85 y, so each step multiplies y by 1 - h*0.85.
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(8.5)=-10.5 and f(11.2)=-9.96.
3. The interval width is 2.7.
Final: {"answer": -27.621, "unit": "area_units"}

Answer: -27.621

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.2x+-12.2 from x=8.5 to x=11.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.5)=-10.5 and f(11.2)=-9.96.
The interval width is 2.7.


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=0.2 and add it to the current value.
Final: {"answer": [-0.69, 1.91, 1.96], "unit": "temperature_units"}

Answer: -0.69

Answer: 1.91

Answer: 1.96

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=-1.55; current interior values are [-1.7, 2.8, 2.85]. 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. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4776.0 / 100.
Final: {"answer": 47.76, "unit": "m"}

Answer: 47.76

Prompt: Convert 4776 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 4776.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=37 degrees and keep the unit as newtons.
Final: {"answer": [262.3518, 197.6962], "unit": "N"}

Answer: 262.3518

Answer: 197.6962

Prompt: A vector has magnitude 328.5 N at 37 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=37 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.4, -29.5], "unit": "dimensionless"}

Answer: 6.4

Answer: -29.5

Prompt: A line passes through points (5.5, 5.7) and (11.25, 42.5). 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. 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=0.48 and interior values [-0.2, -1.05, 0.55], 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 = 9.5 kg and a = 10.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 103.55, "unit": "N"}

Answer: 103.55

Prompt: A cart has mass 9.5 kg and measured acceleration 10.9 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 = 10.9 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.68 * 8.314 * 534 / 5.8.
Final: {"answer": 2051.4365, "unit": "kPa"}

Answer: 2051.4365

Prompt: An ideal gas sample has n=2.68 mol, T=534 K, and V=5.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.68 * 8.314 * 534 / 5.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 770 * 1.23 * 85.
Final: {"answer": 80503.5, "unit": "J"}

Answer: 80503.5

Prompt: A 770 g sample has specific heat 1.23 J/(g*K). How much heat is needed to raise its temperature by 85 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 770 * 1.23 * 85.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=193.1 V and R=195.4 ohm.
Final: {"answer": 190.8271, "unit": "W"}

Answer: 190.8271

Prompt: A resistor has resistance 195.4 ohm and voltage 193.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=193.1 V and R=195.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=975 mg, t=354.5 h, and T_half=37.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.3908, "unit": "mg"}

Answer: 1.3908

Prompt: A radioactive sample starts with 975 mg. Its half-life is 37.5 hours. How many mg remain after 354.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=975 mg, t=354.5 h, and T_half=37.5 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 = 6.71 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 392.1324, "unit": "g"}

Answer: 392.1324

Prompt: A sample contains 6.71 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 = 6.71 mol * 58.44 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) = -0.47 y, so each step multiplies y by 1 - h*0.47.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.026, "unit": "state_units"}

Answer: 0.026

Prompt: Use explicit Euler on dy/dt = -0.47 y with y(0)=28.5, step size h=1.15, 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) = -0.47 y, so each step multiplies y by 1 - h*0.47.
Apply that update for 9 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=0.46 and add it to the current value.
Final: {"answer": [1.252, 0.823, 0.129], "unit": "temperature_units"}

Answer: 1.252

Answer: 0.823

Answer: 0.129

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; current interior values are [-0.45, 1.95, 1.9]. 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 39030.0 / 1000.
Final: {"answer": 39.03, "unit": "kg"}

Answer: 39.03

Prompt: Convert 39030 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 39030.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=93 degrees and keep the unit as newtons.
Final: {"answer": [-14.5756, 278.1183], "unit": "N"}

Answer: -14.5756

Answer: 278.1183

Prompt: A vector has magnitude 278.5 N at 93 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=93 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": [3.3, 27.75], "unit": "dimensionless"}

Answer: 3.3

Answer: 27.75

Prompt: A line passes through points (4.75, 43.425) and (6.25, 48.375). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 16400, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
grams cancel with J/(g*K), and kelvin cancels, leaving joules
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

```python
def running_total_003058(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_003058"}

Answer: python_code

Prompt: Write a Python function running_total_003058(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: 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 57.6 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 = 20.9 kg and a = 2.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.25, "unit": "N"}

Answer: 52.25

Prompt: A cart has mass 20.9 kg and measured acceleration 2.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.9 kg and a = 2.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.9^2 and multiply by 0.5 * 17.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6494.3997, "unit": "J"}

Answer: 6494.3997

Prompt: A body of mass 17.95 kg moves at 26.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.9^2 and multiply by 0.5 * 17.95.
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=80 degrees through the sine of 2 theta.
3. Substitute v=55.9 m/s and g=9.81 m/s^2.
Final: {"answer": 108.9447, "unit": "m"}

Answer: 108.9447

Prompt: A projectile is launched on level ground with no air resistance at speed 55.9 m/s and angle 80 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=80 degrees through the sine of 2 theta.
Substitute v=55.9 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 = 1310 * 2.76 * 26.
Final: {"answer": 94005.6, "unit": "J"}

Answer: 94005.6

Prompt: A 1310 g sample has specific heat 2.76 J/(g*K). How much heat is needed to raise its temperature by 26 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1310 * 2.76 * 26.


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=87.2 V and R=122.7 ohm.
Final: {"answer": 61.971, "unit": "W"}

Answer: 61.971

Prompt: A resistor has resistance 122.7 ohm and voltage 87.2 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=87.2 V and R=122.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=897.5 mg, t=357 h, and T_half=75 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 33.1232, "unit": "mg"}

Answer: 33.1232

Prompt: A radioactive sample starts with 897.5 mg. Its half-life is 75 hours. How many mg remain after 357 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=897.5 mg, t=357 h, and T_half=75 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 4655 mL to 4.655 L.
3. Compute M = 4.385 / 4.655.
Final: {"answer": 0.942, "unit": "mol/L"}

Answer: 0.942

Prompt: A solution contains 4.385 mol of solute in 4655 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4655 mL to 4.655 L.
Compute M = 4.385 / 4.655.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.8678, "unit": "state_units"}

Answer: 0.8678

Prompt: Use explicit Euler on dy/dt = -0.45 y with y(0)=70.5, step size h=1.3, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
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(8.5)=-59.65 and f(16.6)=-104.2.
3. The interval width is 8.1.
Final: {"answer": -663.5925, "unit": "area_units"}

Answer: -663.5925

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+-12.9 from x=8.5 to x=16.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.5)=-59.65 and f(16.6)=-104.2.
The interval width is 8.1.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 22.5 + 273.15.
Final: {"answer": 295.65, "unit": "K"}

Answer: 295.65

Prompt: Convert 22.5 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 22.5 + 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": [6.25, -27.0], "unit": "dimensionless"}

Answer: 6.25

Answer: -27.0

Prompt: A line passes through points (-15.25, -122.312) and (-1.75, -37.9375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In simulation spec case 67004, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def running_total_003076(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_003076"}

Answer: python_code

Prompt: Write a Python function running_total_003076(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: 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 2157 items and budget 58565, 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 = 21 kg and a = 5.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 114.45, "unit": "N"}

Answer: 114.45

Prompt: A cart has mass 21 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 = 21 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 = 20.85^2 and multiply by 0.5 * 24.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5347.0868, "unit": "J"}

Answer: 5347.0868

Prompt: A body of mass 24.6 kg moves at 20.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 20.85^2 and multiply by 0.5 * 24.6.
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=31 degrees through the sine of 2 theta.
3. Substitute v=76.7 m/s and g=9.81 m/s^2.
Final: {"answer": 529.4886, "unit": "m"}

Answer: 529.4886

Prompt: A projectile is launched on level ground with no air resistance at speed 76.7 m/s and angle 31 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=31 degrees through the sine of 2 theta.
Substitute v=76.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=391.5 mg, t=112.5 h, and T_half=35 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 42.1828, "unit": "mg"}

Answer: 42.1828

Prompt: A radioactive sample starts with 391.5 mg. Its half-life is 35 hours. How many mg remain after 112.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=391.5 mg, t=112.5 h, and T_half=35 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 = 3.05 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 54.9457, "unit": "g"}

Answer: 54.9457

Prompt: A sample contains 3.05 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 = 3.05 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2740 mL to 2.74 L.
3. Compute M = 2.02 / 2.74.
Final: {"answer": 0.7372, "unit": "mol/L"}

Answer: 0.7372

Prompt: A solution contains 2.02 mol of solute in 2740 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2740 mL to 2.74 L.
Compute M = 2.02 / 2.74.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.98 y, so each step multiplies y by 1 - h*0.98.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.98 y with y(0)=44, step size h=1.2, 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) = -0.98 y, so each step multiplies y by 1 - h*0.98.
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(-7.4)=-31.96 and f(0.3)=-5.78.
3. The interval width is 7.7.
Final: {"answer": -145.299, "unit": "area_units"}

Answer: -145.299

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.4x+-6.8 from x=-7.4 to x=0.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.4)=-31.96 and f(0.3)=-5.78.
The interval width is 7.7.


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=0.2 and add it to the current value.
Final: {"answer": [1.3, 1.35, -0.28], "unit": "temperature_units"}

Answer: 1.3

Answer: 1.35

Answer: -0.28

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.05, right=0.55; current interior values are [1.4, 2.25, -1.4]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 35142.0 / 1000.
Final: {"answer": 35.142, "unit": "kg"}

Answer: 35.142

Prompt: Convert 35142 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 35142.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=94 degrees and keep the unit as newtons.
Final: {"answer": [-23.9265, 342.1645], "unit": "N"}

Answer: -23.9265

Answer: 342.1645

Prompt: A vector has magnitude 343 N at 94 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=94 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.25, -9.25], "unit": "dimensionless"}

Answer: 4.25

Answer: -9.25

Prompt: A line passes through points (11.5, 39.625) and (13, 46). 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 field worksheet case 226409, 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 clamp_003094(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003094"}

Answer: python_code

Prompt: Write a Python function clamp_003094(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_003094(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: 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 laboratory invoice records in release 365033, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.5 kg and a = 14.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 133.95, "unit": "N"}

Answer: 133.95

Prompt: A cart has mass 9.5 kg and measured acceleration 14.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.5 kg and a = 14.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 330 * 2.445 * 5.
Final: {"answer": 4034.25, "unit": "J"}

Answer: 4034.25

Prompt: A 330 g sample has specific heat 2.445 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 330 * 2.445 * 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=201.6 V and R=67.1 ohm.
Final: {"answer": 605.7013, "unit": "W"}

Answer: 605.7013

Prompt: A resistor has resistance 67.1 ohm and voltage 201.6 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=201.6 V and R=67.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=399.5 mg, t=76 h, and T_half=104 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 240.7317, "unit": "mg"}

Answer: 240.7317

Prompt: A radioactive sample starts with 399.5 mg. Its half-life is 104 hours. How many mg remain after 76 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=399.5 mg, t=76 h, and T_half=104 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 = 0.26 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 46.8406, "unit": "g"}

Answer: 46.8406

Prompt: A sample contains 0.26 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.26 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 1120 mL to 1.12 L.
3. Compute M = 4.82 / 1.12.
Final: {"answer": 4.3036, "unit": "mol/L"}

Answer: 4.3036

Prompt: A solution contains 4.82 mol of solute in 1120 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1120 mL to 1.12 L.
Compute M = 4.82 / 1.12.


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)=55.5, step size h=1.4, 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(-8.8)=76.06 and f(1.1)=9.73.
3. The interval width is 9.9.
Final: {"answer": 424.6605, "unit": "area_units"}

Answer: 424.6605

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+17.1 from x=-8.8 to x=1.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.8)=76.06 and f(1.1)=9.73.
The interval width is 9.9.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.6, 10.25], "unit": "dimensionless"}

Answer: -1.6

Answer: 10.25

Prompt: A line passes through points (-11.75, 29.05) and (3, 5.45). 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.