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 quality-control check case 806532, 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 center_values_007144(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_007144"}

Answer: python_code

Prompt: Write a Python function center_values_007144(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_007144([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing invoice records in release 155638, 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 = 4.5 kg and a = 14.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 67.05, "unit": "N"}

Answer: 67.05

Prompt: A cart has mass 4.5 kg and measured acceleration 14.9 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 = 4.5 kg and a = 14.9 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 = 32.25^2 and multiply by 0.5 * 25.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13390.8047, "unit": "J"}

Answer: 13390.8047

Prompt: A body of mass 25.75 kg moves at 32.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.25^2 and multiply by 0.5 * 25.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.99 * 8.314 * 314 / 49.6.
Final: {"answer": 262.6386, "unit": "kPa"}

Answer: 262.6386

Prompt: An ideal gas sample has n=4.99 mol, T=314 K, and V=49.6 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 = 4.99 * 8.314 * 314 / 49.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1480 * 3.545 * 12.
Final: {"answer": 62959.2, "unit": "J"}

Answer: 62959.2

Prompt: A 1480 g sample has specific heat 3.545 J/(g*K). How much heat is needed to raise its temperature by 12 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1480 * 3.545 * 12.


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=141.1 V and R=135.8 ohm.
Final: {"answer": 146.6068, "unit": "W"}

Answer: 146.6068

Prompt: A resistor has resistance 135.8 ohm and voltage 141.1 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=141.1 V and R=135.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=978.5 mg, t=83.5 h, and T_half=2 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 978.5 mg. Its half-life is 2 hours. How many mg remain after 83.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=978.5 mg, t=83.5 h, and T_half=2 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 65 mL to 0.065 L.
3. Compute M = 0.13 / 0.065.
Final: {"answer": 2.0, "unit": "mol/L"}

Answer: 2.0

Prompt: A solution contains 0.13 mol of solute in 65 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 65 mL to 0.065 L.
Compute M = 0.13 / 0.065.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.6)=54.94 and f(-2.5)=22.55.
3. The interval width is 4.1.
Final: {"answer": 158.8545, "unit": "area_units"}

Answer: 158.8545

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.9x+2.8 from x=-6.6 to x=-2.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.6)=54.94 and f(-2.5)=22.55.
The interval width is 4.1.

(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 46822.0 / 1000.
Final: {"answer": 46.822, "unit": "kg"}

Answer: 46.822

Prompt: Convert 46822 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 46822.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=89 degrees and keep the unit as newtons.
Final: {"answer": [6.6232, 379.4422], "unit": "N"}

Answer: 6.6232

Answer: 379.4422

Prompt: A vector has magnitude 379.5 N at 89 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=89 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": [2.15, 4.75], "unit": "dimensionless"}

Answer: 2.15

Answer: 4.75

Prompt: A line passes through points (2, 9.05) and (3.75, 12.8125). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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_007162(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_007162"}

Answer: python_code

Prompt: Write a Python function threshold_flags_007162(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_007162([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_007162([], 5) == []

assert threshold_flags_007162([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=71 and h=1.4, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 19.7 kg and a = 3.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 64.025, "unit": "N"}

Answer: 64.025

Prompt: A cart has mass 19.7 kg and measured acceleration 3.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 19.7 kg and a = 3.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 11.85^2 and multiply by 0.5 * 17.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1214.6546, "unit": "J"}

Answer: 1214.6546

Prompt: A body of mass 17.3 kg moves at 11.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.85^2 and multiply by 0.5 * 17.3.
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=80 degrees through the sine of 2 theta.
3. Substitute v=51.7 m/s and g=9.81 m/s^2.
Final: {"answer": 93.1888, "unit": "m"}

Answer: 93.1888

Prompt: A projectile is launched on level ground with no air resistance at speed 51.7 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=51.7 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 = 5.72 * 8.314 * 419 / 65.0.
Final: {"answer": 306.5538, "unit": "kPa"}

Answer: 306.5538

Prompt: An ideal gas sample has n=5.72 mol, T=419 K, and V=65.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.72 * 8.314 * 419 / 65.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 510 * 1.47 * 110.
Final: {"answer": 82467.0, "unit": "J"}

Answer: 82467.0

Prompt: A 510 g sample has specific heat 1.47 J/(g*K). How much heat is needed to raise its temperature by 110 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 510 * 1.47 * 110.


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=74 V and R=66.8 ohm.
Final: {"answer": 81.976, "unit": "W"}

Answer: 81.976

Prompt: A resistor has resistance 66.8 ohm and voltage 74 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=74 V and R=66.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=767 mg, t=309 h, and T_half=11 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 767 mg. Its half-life is 11 hours. How many mg remain after 309 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=767 mg, t=309 h, and T_half=11 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 200 mL to 0.2 L.
3. Compute M = 1.455 / 0.2.
Final: {"answer": 7.275, "unit": "mol/L"}

Answer: 7.275

Prompt: A solution contains 1.455 mol of solute in 200 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 200 mL to 0.2 L.
Compute M = 1.455 / 0.2.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 61.4462, "unit": "state_units"}

Answer: 61.4462

Prompt: Use explicit Euler on dy/dt = -0.04 y with y(0)=65, step size h=0.2, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
Apply that update for 7 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)=-17.3 and f(7.1)=-3.81.
3. The interval width is 7.1.
Final: {"answer": -74.9405, "unit": "area_units"}

Answer: -74.9405

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-17.3 from x=0 to x=7.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0)=-17.3 and f(7.1)=-3.81.
The interval width is 7.1.


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": [-9.8705, 141.1553], "unit": "N"}

Answer: -9.8705

Answer: 141.1553

Prompt: A vector has magnitude 141.5 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": [-7.0, 9.5], "unit": "dimensionless"}

Answer: -7.0

Answer: 9.5

Prompt: A line passes through points (10.5, -64) and (18, -116.5). 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. 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 quality-control check case 114550, 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_007180(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007180"}

Answer: python_code

Prompt: Write a Python function running_total_007180(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: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=73.5 and h=1.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.3 kg and a = 14.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 225.675, "unit": "N"}

Answer: 225.675

Prompt: A cart has mass 15.3 kg and measured acceleration 14.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 15.3 kg and a = 14.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 24^2 and multiply by 0.5 * 23.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6782.4, "unit": "J"}

Answer: 6782.4

Prompt: A body of mass 23.55 kg moves at 24 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24^2 and multiply by 0.5 * 23.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=24 degrees through the sine of 2 theta.
3. Substitute v=32.9 m/s and g=9.81 m/s^2.
Final: {"answer": 81.9967, "unit": "m"}

Answer: 81.9967

Prompt: A projectile is launched on level ground with no air resistance at speed 32.9 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=24 degrees through the sine of 2 theta.
Substitute v=32.9 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 = 1115 * 4.065 * 24.
Final: {"answer": 108779.4, "unit": "J"}

Answer: 108779.4

Prompt: A 1115 g sample has specific heat 4.065 J/(g*K). How much heat is needed to raise its temperature by 24 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1115 * 4.065 * 24.


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=191.6 V and R=15.8 ohm.
Final: {"answer": 2323.4532, "unit": "W"}

Answer: 2323.4532

Prompt: A resistor has resistance 15.8 ohm and voltage 191.6 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=191.6 V and R=15.8 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 665 mL to 0.665 L.
3. Compute M = 4.435 / 0.665.
Final: {"answer": 6.6692, "unit": "mol/L"}

Answer: 6.6692

Prompt: A solution contains 4.435 mol of solute in 665 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 665 mL to 0.665 L.
Compute M = 4.435 / 0.665.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.7406, "unit": "state_units"}

Answer: 0.7406

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=1, step size h=0.2, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.5)=-3.35 and f(-3.6)=1.78.
3. The interval width is 1.9.
Final: {"answer": -1.4915, "unit": "area_units"}

Answer: -1.4915

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.7x+11.5 from x=-5.5 to x=-3.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.5)=-3.35 and f(-3.6)=1.78.
The interval width is 1.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [0.789, -1.269, 1.787], "unit": "temperature_units"}

Answer: 0.789

Answer: -1.269

Answer: 1.787

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=-0.6, right=2.1; current interior values are [1.05, -1.65, 2.0]. Use r=0.06. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.06 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 469.5 / 100.
Final: {"answer": 4.695, "unit": "m"}

Answer: 4.695

Prompt: Convert 469.5 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 469.5 / 100.


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

Answer: consistent

Prompt: In student derivation case 500729, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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_007198(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_007198"}

Answer: python_code

Prompt: Write a Python function threshold_flags_007198(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_007198([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_007198([], 5) == []

assert threshold_flags_007198([-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: 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 allocation scoring problem with 2831 items and budget 31520, 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 = 13.95 kg and a = 5.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 71.8425, "unit": "N"}

Answer: 71.8425

Prompt: A cart has mass 13.95 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 13.95 kg and a = 5.15 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 = 28.85^2 and multiply by 0.5 * 22.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9217.9717, "unit": "J"}

Answer: 9217.9717

Prompt: A body of mass 22.15 kg moves at 28.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 28.85^2 and multiply by 0.5 * 22.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=84 degrees through the sine of 2 theta.
3. Substitute v=77 m/s and g=9.81 m/s^2.
Final: {"answer": 125.6584, "unit": "m"}

Answer: 125.6584

Prompt: A projectile is launched on level ground with no air resistance at speed 77 m/s and angle 84 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=84 degrees through the sine of 2 theta.
Substitute v=77 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.98 * 8.314 * 381 / 35.9.
Final: {"answer": 351.175, "unit": "kPa"}

Answer: 351.175

Prompt: An ideal gas sample has n=3.98 mol, T=381 K, and V=35.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.98 * 8.314 * 381 / 35.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 725 * 4.1 * 38.
Final: {"answer": 112955.0, "unit": "J"}

Answer: 112955.0

Prompt: A 725 g sample has specific heat 4.1 J/(g*K). How much heat is needed to raise its temperature by 38 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 725 * 4.1 * 38.


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=1.5 V and R=97.4 ohm.
Final: {"answer": 0.0231, "unit": "W"}

Answer: 0.0231

Prompt: A resistor has resistance 97.4 ohm and voltage 1.5 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=1.5 V and R=97.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=792.5 mg, t=235 h, and T_half=79.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 102.1321, "unit": "mg"}

Answer: 102.1321

Prompt: A radioactive sample starts with 792.5 mg. Its half-life is 79.5 hours. How many mg remain after 235 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=792.5 mg, t=235 h, and T_half=79.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.89 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 259.2189, "unit": "g"}

Answer: 259.2189

Prompt: A sample contains 5.89 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.89 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 3090 mL to 3.09 L.
3. Compute M = 2.39 / 3.09.
Final: {"answer": 0.7735, "unit": "mol/L"}

Answer: 0.7735

Prompt: A solution contains 2.39 mol of solute in 3090 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3090 mL to 3.09 L.
Compute M = 2.39 / 3.09.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.72 y, so each step multiplies y by 1 - h*0.72.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.1396, "unit": "state_units"}

Answer: 0.1396

Prompt: Use explicit Euler on dy/dt = -0.72 y with y(0)=14, step size h=0.95, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.72 y, so each step multiplies y by 1 - h*0.72.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.3)=18.81 and f(7.9)=40.43.
3. The interval width is 4.6.
Final: {"answer": 136.252, "unit": "area_units"}

Answer: 136.252

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+3.3 from x=3.3 to x=7.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.3)=18.81 and f(7.9)=40.43.
The interval width is 4.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [1.286, -1.024, 0.066], "unit": "temperature_units"}

Answer: 1.286

Answer: -1.024

Answer: 0.066

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, right=-0.6; current interior values are [-1.45, 0.8, -0.75]. Use r=0.48. 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=0.48 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 68.5 + 273.15.
Final: {"answer": 341.65, "unit": "K"}

Answer: 341.65

Prompt: Convert 68.5 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 68.5 + 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=299 degrees and keep the unit as newtons.
Final: {"answer": [107.3853, -193.7283], "unit": "N"}

Answer: 107.3853

Answer: -193.7283

Prompt: A vector has magnitude 221.5 N at 299 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=299 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.5, -23.25], "unit": "dimensionless"}

Answer: -1.5

Answer: -23.25

Prompt: A line passes through points (18.5, -51) and (23.5, -58.5). 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. 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 student derivation case 693670, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid warehouse clinical records in release 232161, 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 = 16 kg and a = 8.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 129.6, "unit": "N"}

Answer: 129.6

Prompt: A cart has mass 16 kg and measured acceleration 8.1 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 = 16 kg and a = 8.1 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 = 2.55^2 and multiply by 0.5 * 26.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 85.0202, "unit": "J"}

Answer: 85.0202

Prompt: A body of mass 26.15 kg moves at 2.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.55^2 and multiply by 0.5 * 26.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=34 degrees through the sine of 2 theta.
3. Substitute v=71.7 m/s and g=9.81 m/s^2.
Final: {"answer": 485.8869, "unit": "m"}

Answer: 485.8869

Prompt: A projectile is launched on level ground with no air resistance at speed 71.7 m/s and angle 34 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=34 degrees through the sine of 2 theta.
Substitute v=71.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.48 * 8.314 * 393 / 59.8.
Final: {"answer": 244.782, "unit": "kPa"}

Answer: 244.782

Prompt: An ideal gas sample has n=4.48 mol, T=393 K, and V=59.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.48 * 8.314 * 393 / 59.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 910 * 1.925 * 58.
Final: {"answer": 101601.5, "unit": "J"}

Answer: 101601.5

Prompt: A 910 g sample has specific heat 1.925 J/(g*K). How much heat is needed to raise its temperature by 58 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 910 * 1.925 * 58.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=966.5 mg, t=51.5 h, and T_half=107.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 693.4058, "unit": "mg"}

Answer: 693.4058

Prompt: A radioactive sample starts with 966.5 mg. Its half-life is 107.5 hours. How many mg remain after 51.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=966.5 mg, t=51.5 h, and T_half=107.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.68 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 12.2502, "unit": "g"}

Answer: 12.2502

Prompt: A sample contains 0.68 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.68 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 550 mL to 0.55 L.
3. Compute M = 1.645 / 0.55.
Final: {"answer": 2.9909, "unit": "mol/L"}

Answer: 2.9909

Prompt: A solution contains 1.645 mol of solute in 550 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 550 mL to 0.55 L.
Compute M = 1.645 / 0.55.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.
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 = -0.9 y with y(0)=40, 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) = -0.9 y, so each step multiplies y by 1 - h*0.9.
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(9.1)=72.84 and f(9.6)=76.54.
3. The interval width is 0.5.
Final: {"answer": 37.345, "unit": "area_units"}

Answer: 37.345

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.4x+5.5 from x=9.1 to x=9.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.1)=72.84 and f(9.6)=76.54.
The interval width is 0.5.


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=0.42 and add it to the current value.
Final: {"answer": [-0.99, 1.046, 0.099], "unit": "temperature_units"}

Answer: -0.99

Answer: 1.046

Answer: 0.099

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=-1.75, right=-0.3; current interior values are [-0.15, -0.55, 2.85]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=68 degrees and keep the unit as newtons.
Final: {"answer": [112.1947, 277.6916], "unit": "N"}

Answer: 112.1947

Answer: 277.6916

Prompt: A vector has magnitude 299.5 N at 68 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=68 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": [-8.1, -16.0], "unit": "dimensionless"}

Answer: -8.1

Answer: -16.0

Prompt: A line passes through points (-1.75, -1.825) and (12, -113.2). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def weighted_sum_007234(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_007234"}

Answer: python_code

Prompt: Write a Python function weighted_sum_007234(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_007234([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 knapsack scoring problem with 3957 items and budget 82785, 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 = 1.95 kg and a = 15.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 30.03, "unit": "N"}

Answer: 30.03

Prompt: A cart has mass 1.95 kg and measured acceleration 15.4 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 = 1.95 kg and a = 15.4 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 = 34.2^2 and multiply by 0.5 * 11.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6637.707, "unit": "J"}

Answer: 6637.707

Prompt: A body of mass 11.35 kg moves at 34.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.2^2 and multiply by 0.5 * 11.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=210 mg, t=79.5 h, and T_half=35.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 44.4715, "unit": "mg"}

Answer: 44.4715

Prompt: A radioactive sample starts with 210 mg. Its half-life is 35.5 hours. How many mg remain after 79.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=210 mg, t=79.5 h, and T_half=35.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.79 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1043.1032, "unit": "g"}

Answer: 1043.1032

Prompt: A sample contains 5.79 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.79 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 1695 mL to 1.695 L.
3. Compute M = 1.16 / 1.695.
Final: {"answer": 0.6844, "unit": "mol/L"}

Answer: 0.6844

Prompt: A solution contains 1.16 mol of solute in 1695 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1695 mL to 1.695 L.
Compute M = 1.16 / 1.695.


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 5 steps and round the final state.
Final: {"answer": 0.0008, "unit": "state_units"}

Answer: 0.0008

Prompt: Use explicit Euler on dy/dt = -0.47 y with y(0)=60.5, step size h=1.9, 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) = -0.47 y, so each step multiplies y by 1 - h*0.47.
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(-5.4)=-3.14 and f(0.7)=21.87.
3. The interval width is 6.1.
Final: {"answer": 57.1265, "unit": "area_units"}

Answer: 57.1265

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+19 from x=-5.4 to x=0.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.4)=-3.14 and f(0.7)=21.87.
The interval width is 6.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.36 and add it to the current value.
Final: {"answer": [-0.526, 0.328, -0.472], "unit": "temperature_units"}

Answer: -0.526

Answer: 0.328

Answer: -0.472

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=-1.4, right=0.5; current interior values are [2.3, -1.85, 0.05]. 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 4531.5 / 100.
Final: {"answer": 45.315, "unit": "m"}

Answer: 45.315

Prompt: Convert 4531.5 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 4531.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=53 degrees and keep the unit as newtons.
Final: {"answer": [124.2748, 164.9182], "unit": "N"}

Answer: 124.2748

Answer: 164.9182

Prompt: A vector has magnitude 206.5 N at 53 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=53 degrees and keep the unit as newtons.


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 quality-control check case 870696, 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 finite_differences_007252(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_007252"}

Answer: python_code

Prompt: Write a Python function finite_differences_007252(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_007252([5]) == []

assert finite_differences_007252([]) == []


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=52 degrees through the sine of 2 theta.
3. Substitute v=24.5 m/s and g=9.81 m/s^2.
Final: {"answer": 59.37, "unit": "m"}

Answer: 59.37

Prompt: A projectile is launched on level ground with no air resistance at speed 24.5 m/s and angle 52 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=52 degrees through the sine of 2 theta.
Substitute v=24.5 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 = 2.36 * 8.314 * 298 / 114.0.
Final: {"answer": 51.2901, "unit": "kPa"}

Answer: 51.2901

Prompt: An ideal gas sample has n=2.36 mol, T=298 K, and V=114.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.36 * 8.314 * 298 / 114.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1750 * 4.115 * 6.
Final: {"answer": 43207.5, "unit": "J"}

Answer: 43207.5

Prompt: A 1750 g sample has specific heat 4.115 J/(g*K). How much heat is needed to raise its temperature by 6 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1750 * 4.115 * 6.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=194.5 V and R=145.3 ohm.
Final: {"answer": 260.3596, "unit": "W"}

Answer: 260.3596

Prompt: A resistor has resistance 145.3 ohm and voltage 194.5 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=194.5 V and R=145.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=364.5 mg, t=216.5 h, and T_half=88.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 66.8774, "unit": "mg"}

Answer: 66.8774

Prompt: A radioactive sample starts with 364.5 mg. Its half-life is 88.5 hours. How many mg remain after 216.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=364.5 mg, t=216.5 h, and T_half=88.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0817, "unit": "state_units"}

Answer: 0.0817

Prompt: Use explicit Euler on dy/dt = -0.71 y with y(0)=74, step size h=0.65, 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) = -0.71 y, so each step multiplies y by 1 - h*0.71.
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=0.2 and add it to the current value.
Final: {"answer": [1.22, 1.77, 0.05], "unit": "temperature_units"}

Answer: 1.22

Answer: 1.77

Answer: 0.05

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=-1.2, right=-0.45; current interior values are [1.55, 2.65, -0.65]. Use r=0.2. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=106 degrees and keep the unit as newtons.
Final: {"answer": [-77.5919, 270.5952], "unit": "N"}

Answer: -77.5919

Answer: 270.5952

Prompt: A vector has magnitude 281.5 N at 106 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=106 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.45, 28.0], "unit": "dimensionless"}

Answer: 7.45

Answer: 28.0

Prompt: A line passes through points (10.5, 106.225) and (22, 191.9). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 909932, 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_007270(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007270"}

Answer: python_code

Prompt: Write a Python function running_total_007270(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=0.47 mol and T=456 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.1 kg and a = 5.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 28.56, "unit": "N"}

Answer: 28.56

Prompt: A cart has mass 5.1 kg and measured acceleration 5.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.1 kg and a = 5.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 22^2 and multiply by 0.5 * 13.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3327.5, "unit": "J"}

Answer: 3327.5

Prompt: A body of mass 13.75 kg moves at 22 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 22^2 and multiply by 0.5 * 13.75.
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=66 degrees through the sine of 2 theta.
3. Substitute v=73.8 m/s and g=9.81 m/s^2.
Final: {"answer": 412.5886, "unit": "m"}

Answer: 412.5886

Prompt: A projectile is launched on level ground with no air resistance at speed 73.8 m/s and angle 66 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=66 degrees through the sine of 2 theta.
Substitute v=73.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.27 * 8.314 * 270 / 5.3.
Final: {"answer": 1384.9869, "unit": "kPa"}

Answer: 1384.9869

Prompt: An ideal gas sample has n=3.27 mol, T=270 K, and V=5.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.27 * 8.314 * 270 / 5.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 560 * 0.545 * 14.
Final: {"answer": 4272.8, "unit": "J"}

Answer: 4272.8

Prompt: A 560 g sample has specific heat 0.545 J/(g*K). How much heat is needed to raise its temperature by 14 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 560 * 0.545 * 14.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=125.3 V and R=165.8 ohm.
Final: {"answer": 94.6929, "unit": "W"}

Answer: 94.6929

Prompt: A resistor has resistance 165.8 ohm and voltage 125.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=125.3 V and R=165.8 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.06 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1.0809, "unit": "g"}

Answer: 1.0809

Prompt: A sample contains 0.06 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.06 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 4020 mL to 4.02 L.
3. Compute M = 1.75 / 4.02.
Final: {"answer": 0.4353, "unit": "mol/L"}

Answer: 0.4353

Prompt: A solution contains 1.75 mol of solute in 4020 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4020 mL to 4.02 L.
Compute M = 1.75 / 4.02.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0078, "unit": "state_units"}

Answer: 0.0078

Prompt: Use explicit Euler on dy/dt = -0.35 y with y(0)=59.5, step size h=1.5, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.7)=36.94 and f(-7.6)=34.52.
3. The interval width is 1.1.
Final: {"answer": 39.303, "unit": "area_units"}

Answer: 39.303

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+17.8 from x=-8.7 to x=-7.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.7)=36.94 and f(-7.6)=34.52.
The interval width is 1.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [1.547, 1.407, 1.644], "unit": "temperature_units"}

Answer: 1.547

Answer: 1.407

Answer: 1.644

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=0.9; current interior values are [1.3, 0.9, 2.45]. Use r=0.26. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3891.5 / 100.
Final: {"answer": 38.915, "unit": "m"}

Answer: 38.915

Prompt: Convert 3891.5 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 3891.5 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.75, -16.0], "unit": "dimensionless"}

Answer: -9.75

Answer: -16.0

Prompt: A line passes through points (-4.25, 25.4375) and (-0.75, -8.6875). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In student derivation case 892858, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.5 kg and a = 5.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 59.85, "unit": "N"}

Answer: 59.85

Prompt: A cart has mass 10.5 kg and measured acceleration 5.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.5 kg and a = 5.7 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 = 18.7^2 and multiply by 0.5 * 8.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1494.9248, "unit": "J"}

Answer: 1494.9248

Prompt: A body of mass 8.55 kg moves at 18.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.7^2 and multiply by 0.5 * 8.55.
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=19 degrees through the sine of 2 theta.
3. Substitute v=36.7 m/s and g=9.81 m/s^2.
Final: {"answer": 84.5289, "unit": "m"}

Answer: 84.5289

Prompt: A projectile is launched on level ground with no air resistance at speed 36.7 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=19 degrees through the sine of 2 theta.
Substitute v=36.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.48 * 8.314 * 352 / 8.8.
Final: {"answer": 1822.4288, "unit": "kPa"}

Answer: 1822.4288

Prompt: An ideal gas sample has n=5.48 mol, T=352 K, and V=8.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.48 * 8.314 * 352 / 8.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1945 * 4.775 * 92.
Final: {"answer": 854438.5, "unit": "J"}

Answer: 854438.5

Prompt: A 1945 g sample has specific heat 4.775 J/(g*K). How much heat is needed to raise its temperature by 92 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1945 * 4.775 * 92.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=780 mg, t=95 h, and T_half=118 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 446.4162, "unit": "mg"}

Answer: 446.4162

Prompt: A radioactive sample starts with 780 mg. Its half-life is 118 hours. How many mg remain after 95 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=780 mg, t=95 h, and T_half=118 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 = 4.31 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 77.6446, "unit": "g"}

Answer: 77.6446

Prompt: A sample contains 4.31 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.31 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 4485 mL to 4.485 L.
3. Compute M = 0.675 / 4.485.
Final: {"answer": 0.1505, "unit": "mol/L"}

Answer: 0.1505

Prompt: A solution contains 0.675 mol of solute in 4485 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4485 mL to 4.485 L.
Compute M = 0.675 / 4.485.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.5)=-7.95 and f(8.3)=-10.65.
3. The interval width is 1.8.
Final: {"answer": -16.74, "unit": "area_units"}

Answer: -16.74

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+1.8 from x=6.5 to x=8.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.5)=-7.95 and f(8.3)=-10.65.
The interval width is 1.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.18 and add it to the current value.
Final: {"answer": [0.192, 1.255, 2.329], "unit": "temperature_units"}

Answer: 0.192

Answer: 1.255

Answer: 2.329

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=0.3, right=2.75; current interior values are [-0.15, 1.3, 2.5]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 36205.0 / 1000.
Final: {"answer": 36.205, "unit": "kg"}

Answer: 36.205

Prompt: Convert 36205 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 36205.0 / 1000.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In model card equation case 896461, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
coulomb per second is ampere
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 normalize_007306(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_007306"}

Answer: python_code

Prompt: Write a Python function normalize_007306(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_007306([2, 3, 5]); assert len(out) == 3

try:
    normalize_007306([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: 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 sensor records in release 199333, 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 = 10.3 kg and a = 7.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 77.765, "unit": "N"}

Answer: 77.765

Prompt: A cart has mass 10.3 kg and measured acceleration 7.55 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 = 10.3 kg and a = 7.55 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 = 31.9^2 and multiply by 0.5 * 23.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11804.276, "unit": "J"}

Answer: 11804.276

Prompt: A body of mass 23.2 kg moves at 31.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.9^2 and multiply by 0.5 * 23.2.
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=83 degrees through the sine of 2 theta.
3. Substitute v=50.8 m/s and g=9.81 m/s^2.
Final: {"answer": 63.6405, "unit": "m"}

Answer: 63.6405

Prompt: A projectile is launched on level ground with no air resistance at speed 50.8 m/s and angle 83 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=83 degrees through the sine of 2 theta.
Substitute v=50.8 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 = 1455 * 1.95 * 103.
Final: {"answer": 292236.75, "unit": "J"}

Answer: 292236.75

Prompt: A 1455 g sample has specific heat 1.95 J/(g*K). How much heat is needed to raise its temperature by 103 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1455 * 1.95 * 103.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=948.5 mg, t=167 h, and T_half=110.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 332.7262, "unit": "mg"}

Answer: 332.7262

Prompt: A radioactive sample starts with 948.5 mg. Its half-life is 110.5 hours. How many mg remain after 167 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=948.5 mg, t=167 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 = 3.23 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 581.9039, "unit": "g"}

Answer: 581.9039

Prompt: A sample contains 3.23 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 = 3.23 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 420 mL to 0.42 L.
3. Compute M = 4.84 / 0.42.
Final: {"answer": 11.5238, "unit": "mol/L"}

Answer: 11.5238

Prompt: A solution contains 4.84 mol of solute in 420 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 420 mL to 0.42 L.
Compute M = 4.84 / 0.42.


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 11 steps and round the final state.
Final: {"answer": 3.6746, "unit": "state_units"}

Answer: 3.6746

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=5.5, step size h=0.4, 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
Apply that update for 11 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(4.2)=-18.36 and f(8.7)=-21.96.
3. The interval width is 4.5.
Final: {"answer": -90.72, "unit": "area_units"}

Answer: -90.72

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.8x+-15 from x=4.2 to x=8.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.2)=-18.36 and f(8.7)=-21.96.
The interval width is 4.5.


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=0.38 and add it to the current value.
Final: {"answer": [-0.037, 0.949, 1.419], "unit": "temperature_units"}

Answer: -0.037

Answer: 0.949

Answer: 1.419

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=2.65; current interior values are [0.4, -0.4, 2.35]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=65 degrees and keep the unit as newtons.
Final: {"answer": [106.9224, 229.2959], "unit": "N"}

Answer: 106.9224

Answer: 229.2959

Prompt: A vector has magnitude 253 N at 65 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=65 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": [2.1, -17.25], "unit": "dimensionless"}

Answer: 2.1

Answer: -17.25

Prompt: A line passes through points (-1.75, -20.925) and (-0.25, -17.775). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 75135, 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. Use Newton's second law F = m a.
2. Substitute m = 10.1 kg and a = 11.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 113.625, "unit": "N"}

Answer: 113.625

Prompt: A cart has mass 10.1 kg and measured acceleration 11.25 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 = 10.1 kg and a = 11.25 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 = 35^2 and multiply by 0.5 * 28.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 17701.25, "unit": "J"}

Answer: 17701.25

Prompt: A body of mass 28.9 kg moves at 35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 35^2 and multiply by 0.5 * 28.9.
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=64 degrees through the sine of 2 theta.
3. Substitute v=17.7 m/s and g=9.81 m/s^2.
Final: {"answer": 25.1657, "unit": "m"}

Answer: 25.1657

Prompt: A projectile is launched on level ground with no air resistance at speed 17.7 m/s and angle 64 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=64 degrees through the sine of 2 theta.
Substitute v=17.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.49 * 8.314 * 448 / 44.4.
Final: {"answer": 376.6617, "unit": "kPa"}

Answer: 376.6617

Prompt: An ideal gas sample has n=4.49 mol, T=448 K, and V=44.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.49 * 8.314 * 448 / 44.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1985 * 1.12 * 1.
Final: {"answer": 2223.2, "unit": "J"}

Answer: 2223.2

Prompt: A 1985 g sample has specific heat 1.12 J/(g*K). How much heat is needed to raise its temperature by 1 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1985 * 1.12 * 1.


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=129.8 V and R=100.3 ohm.
Final: {"answer": 167.9765, "unit": "W"}

Answer: 167.9765

Prompt: A resistor has resistance 100.3 ohm and voltage 129.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=129.8 V and R=100.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=888 mg, t=74.5 h, and T_half=17.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 46.4393, "unit": "mg"}

Answer: 46.4393

Prompt: A radioactive sample starts with 888 mg. Its half-life is 17.5 hours. How many mg remain after 74.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=888 mg, t=74.5 h, and T_half=17.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2535 mL to 2.535 L.
3. Compute M = 2.905 / 2.535.
Final: {"answer": 1.146, "unit": "mol/L"}

Answer: 1.146

Prompt: A solution contains 2.905 mol of solute in 2535 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2535 mL to 2.535 L.
Compute M = 2.905 / 2.535.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0005, "unit": "state_units"}

Answer: 0.0005

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=6.5, step size h=1.1, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.7)=-34.59 and f(0.1)=-7.33.
3. The interval width is 5.8.
Final: {"answer": -121.568, "unit": "area_units"}

Answer: -121.568

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+-7.8 from x=-5.7 to x=0.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.7)=-34.59 and f(0.1)=-7.33.
The interval width is 5.8.


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=0.3 and add it to the current value.
Final: {"answer": [0.925, 0.12, -0.455], "unit": "temperature_units"}

Answer: 0.925

Answer: 0.12

Answer: -0.455

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, right=-1.4; current interior values are [-0.65, 1.95, -1.55]. Use r=0.3. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.3 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 43115.0 / 1000.
Final: {"answer": 43.115, "unit": "kg"}

Answer: 43.115

Prompt: Convert 43115 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 43115.0 / 1000.


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 field worksheet case 741195, 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 center_values_007342(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_007342"}

Answer: python_code

Prompt: Write a Python function center_values_007342(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_007342([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing crop records in release 990617, 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 = 16.45 kg and a = 5.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 84.7175, "unit": "N"}

Answer: 84.7175

Prompt: A cart has mass 16.45 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.45 kg and a = 5.15 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 = 20.25^2 and multiply by 0.5 * 25.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5228.2969, "unit": "J"}

Answer: 5228.2969

Prompt: A body of mass 25.5 kg moves at 20.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 20.25^2 and multiply by 0.5 * 25.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=48 degrees through the sine of 2 theta.
3. Substitute v=28.7 m/s and g=9.81 m/s^2.
Final: {"answer": 83.5044, "unit": "m"}

Answer: 83.5044

Prompt: A projectile is launched on level ground with no air resistance at speed 28.7 m/s and angle 48 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=48 degrees through the sine of 2 theta.
Substitute v=28.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.49 * 8.314 * 538 / 19.7.
Final: {"answer": 565.3604, "unit": "kPa"}

Answer: 565.3604

Prompt: An ideal gas sample has n=2.49 mol, T=538 K, and V=19.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.49 * 8.314 * 538 / 19.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 605 * 4.3 * 60.
Final: {"answer": 156090.0, "unit": "J"}

Answer: 156090.0

Prompt: A 605 g sample has specific heat 4.3 J/(g*K). How much heat is needed to raise its temperature by 60 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 605 * 4.3 * 60.


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=105.9 V and R=101.1 ohm.
Final: {"answer": 110.9279, "unit": "W"}

Answer: 110.9279

Prompt: A resistor has resistance 101.1 ohm and voltage 105.9 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=105.9 V and R=101.1 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.47 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 20.6847, "unit": "g"}

Answer: 20.6847

Prompt: A sample contains 0.47 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.47 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 1055 mL to 1.055 L.
3. Compute M = 1.795 / 1.055.
Final: {"answer": 1.7014, "unit": "mol/L"}

Answer: 1.7014

Prompt: A solution contains 1.795 mol of solute in 1055 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1055 mL to 1.055 L.
Compute M = 1.795 / 1.055.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 62.5165, "unit": "state_units"}

Answer: 62.5165

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=80, step size h=1.45, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
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(-1.5)=5.45 and f(-0.6)=9.14.
3. The interval width is 0.9.
Final: {"answer": 6.5655, "unit": "area_units"}

Answer: 6.5655

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+11.6 from x=-1.5 to x=-0.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.5)=5.45 and f(-0.6)=9.14.
The interval width is 0.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.04 and add it to the current value.
Final: {"answer": [0.34, -1.198, 0.73], "unit": "temperature_units"}

Answer: 0.34

Answer: -1.198

Answer: 0.73

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.8, right=2.35; current interior values are [0.35, -1.35, 0.75]. Use r=0.04. 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=0.04 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=311 degrees and keep the unit as newtons.
Final: {"answer": [196.8177, -226.4129], "unit": "N"}

Answer: 196.8177

Answer: -226.4129

Prompt: A vector has magnitude 300 N at 311 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=311 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": [4.85, 28.75], "unit": "dimensionless"}

Answer: 4.85

Answer: 28.75

Prompt: A line passes through points (-7.75, -8.8375) and (5.25, 54.2125). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In instrument manual case 797101, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_007360(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_007360"}

Answer: python_code

Prompt: Write a Python function safe_mean_007360(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_007360([])
    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 field experiment records in release 469632, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.75^2 and multiply by 0.5 * 25.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 38.7406, "unit": "J"}

Answer: 38.7406

Prompt: A body of mass 25.3 kg moves at 1.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.75^2 and multiply by 0.5 * 25.3.
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=32 degrees through the sine of 2 theta.
3. Substitute v=25 m/s and g=9.81 m/s^2.
Final: {"answer": 57.2626, "unit": "m"}

Answer: 57.2626

Prompt: A projectile is launched on level ground with no air resistance at speed 25 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=32 degrees through the sine of 2 theta.
Substitute v=25 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.13 * 8.314 * 439 / 71.8.
Final: {"answer": 108.2754, "unit": "kPa"}

Answer: 108.2754

Prompt: An ideal gas sample has n=2.13 mol, T=439 K, and V=71.8 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 = 2.13 * 8.314 * 439 / 71.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1695 * 4.235 * 114.
Final: {"answer": 818329.05, "unit": "J"}

Answer: 818329.05

Prompt: A 1695 g sample has specific heat 4.235 J/(g*K). How much heat is needed to raise its temperature by 114 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1695 * 4.235 * 114.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4140 mL to 4.14 L.
3. Compute M = 2.035 / 4.14.
Final: {"answer": 0.4915, "unit": "mol/L"}

Answer: 0.4915

Prompt: A solution contains 2.035 mol of solute in 4140 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4140 mL to 4.14 L.
Compute M = 2.035 / 4.14.