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 = 4.52 * 8.314 * 483 / 60.2.
Final: {"answer": 301.5082, "unit": "kPa"}

Answer: 301.5082

Prompt: An ideal gas sample has n=4.52 mol, T=483 K, and V=60.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.52 * 8.314 * 483 / 60.2.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3455 mL to 3.455 L.
3. Compute M = 3.505 / 3.455.
Final: {"answer": 1.0145, "unit": "mol/L"}

Answer: 1.0145

Prompt: A solution contains 3.505 mol of solute in 3455 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3455 mL to 3.455 L.
Compute M = 3.505 / 3.455.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.4)=18.12 and f(4.2)=21.96.
3. The interval width is 0.8.
Final: {"answer": 16.032, "unit": "area_units"}

Answer: 16.032

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+1.8 from x=3.4 to x=4.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.4)=18.12 and f(4.2)=21.96.
The interval width is 0.8.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=277 degrees and keep the unit as newtons.
Final: {"answer": [6.6419, -54.0938], "unit": "N"}

Answer: 6.6419

Answer: -54.0938

Prompt: A vector has magnitude 54.5 N at 277 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=277 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.5 kg and a = 2.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 48.375, "unit": "N"}

Answer: 48.375

Prompt: A cart has mass 21.5 kg and measured acceleration 2.25 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 = 21.5 kg and a = 2.25 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 = 14.4^2 and multiply by 0.5 * 18.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1876.608, "unit": "J"}

Answer: 1876.608

Prompt: A body of mass 18.1 kg moves at 14.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14.4^2 and multiply by 0.5 * 18.1.
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 = 4.3 * 8.314 * 450 / 53.5.
Final: {"answer": 300.7026, "unit": "kPa"}

Answer: 300.7026

Prompt: An ideal gas sample has n=4.3 mol, T=450 K, and V=53.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.3 * 8.314 * 450 / 53.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 380 * 2.065 * 78.
Final: {"answer": 61206.6, "unit": "J"}

Answer: 61206.6

Prompt: A 380 g sample has specific heat 2.065 J/(g*K). How much heat is needed to raise its temperature by 78 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 380 * 2.065 * 78.


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=112 V and R=147.9 ohm.
Final: {"answer": 84.8141, "unit": "W"}

Answer: 84.8141

Prompt: A resistor has resistance 147.9 ohm and voltage 112 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=112 V and R=147.9 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": -0.4004, "unit": "state_units"}

Answer: -0.4004

Prompt: Use explicit Euler on dy/dt = -0.96 y with y(0)=31.5, step size h=1.6, 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) = -0.96 y, so each step multiplies y by 1 - h*0.96.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=55 degrees through the sine of 2 theta.
3. Substitute v=60.5 m/s and g=9.81 m/s^2.
Final: {"answer": 350.6126, "unit": "m"}

Answer: 350.6126

Prompt: A projectile is launched on level ground with no air resistance at speed 60.5 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=55 degrees through the sine of 2 theta.
Substitute v=60.5 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 = 2.95 * 8.314 * 295 / 64.0.
Final: {"answer": 113.0509, "unit": "kPa"}

Answer: 113.0509

Prompt: An ideal gas sample has n=2.95 mol, T=295 K, and V=64.0 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 = 2.95 * 8.314 * 295 / 64.0.


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=0.1 and add it to the current value.
Final: {"answer": [1.83, -0.355, -0.65], "unit": "temperature_units"}

Answer: 1.83

Answer: -0.355

Answer: -0.65

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.05, right=0.95; current interior values are [2.5, -0.65, -0.85]. Use r=0.1. 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=0.1 and add it to the current value.


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

```python
import math

def unit_vector_000088(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_000088"}

Answer: python_code

Prompt: Write a Python function unit_vector_000088(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.

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

try:
    unit_vector_000088(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1005 * 3.865 * 90.
Final: {"answer": 349589.25, "unit": "J"}

Answer: 349589.25

Prompt: A 1005 g sample has specific heat 3.865 J/(g*K). How much heat is needed to raise its temperature by 90 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1005 * 3.865 * 90.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.84 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 871.955, "unit": "g"}

Answer: 871.955

Prompt: A sample contains 4.84 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.84 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=74 degrees through the sine of 2 theta.
3. Substitute v=65.8 m/s and g=9.81 m/s^2.
Final: {"answer": 233.8797, "unit": "m"}

Answer: 233.8797

Prompt: A projectile is launched on level ground with no air resistance at speed 65.8 m/s and angle 74 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=74 degrees through the sine of 2 theta.
Substitute v=65.8 m/s and g=9.81 m/s^2.


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_000124(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_000124"}

Answer: python_code

Prompt: Write a Python function safe_mean_000124(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_000124([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=334 degrees and keep the unit as newtons.
Final: {"answer": [95.2722, -46.4673], "unit": "N"}

Answer: 95.2722

Answer: -46.4673

Prompt: A vector has magnitude 106 N at 334 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=334 degrees and keep the unit as newtons.


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=50.1 m/s and g=9.81 m/s^2.
Final: {"answer": 229.9676, "unit": "m"}

Answer: 229.9676

Prompt: A projectile is launched on level ground with no air resistance at speed 50.1 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=50.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2820 mL to 2.82 L.
3. Compute M = 1.2 / 2.82.
Final: {"answer": 0.4255, "unit": "mol/L"}

Answer: 0.4255

Prompt: A solution contains 1.2 mol of solute in 2820 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2820 mL to 2.82 L.
Compute M = 1.2 / 2.82.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 89.5 + 273.15.
Final: {"answer": 362.65, "unit": "K"}

Answer: 362.65

Prompt: Convert 89.5 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 89.5 + 273.15.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.65, 23.75], "unit": "dimensionless"}

Answer: -7.65

Answer: 23.75

Prompt: A line passes through points (10.5, -56.575) and (18.75, -119.688). 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. Use Newton's second law F = m a.
2. Substitute m = 23.6 kg and a = 6.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 162.84, "unit": "N"}

Answer: 162.84

Prompt: A cart has mass 23.6 kg and measured acceleration 6.9 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 = 23.6 kg and a = 6.9 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 = 11.6^2 and multiply by 0.5 * 24.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1658.452, "unit": "J"}

Answer: 1658.452

Prompt: A body of mass 24.65 kg moves at 11.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.6^2 and multiply by 0.5 * 24.65.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1900 * 2.595 * 106.
Final: {"answer": 522633.0, "unit": "J"}

Answer: 522633.0

Prompt: A 1900 g sample has specific heat 2.595 J/(g*K). How much heat is needed to raise its temperature by 106 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1900 * 2.595 * 106.


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_000196(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_000196"}

Answer: python_code

Prompt: Write a Python function center_values_000196(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_000196([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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": [-4.55, 22.5], "unit": "dimensionless"}

Answer: -4.55

Answer: 22.5

Prompt: A line passes through points (-12.5, 79.375) and (-0.25, 23.6375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 508093, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.6, 10.0], "unit": "dimensionless"}

Answer: -4.6

Answer: 10.0

Prompt: A line passes through points (5.25, -14.15) and (14.25, -55.55). 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. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 970 * 4.345 * 21.
Final: {"answer": 88507.65, "unit": "J"}

Answer: 88507.65

Prompt: A 970 g sample has specific heat 4.345 J/(g*K). How much heat is needed to raise its temperature by 21 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 970 * 4.345 * 21.


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 instrument manual case 721824, 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 8.65^2 and multiply by 0.5 * 25.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 963.3397, "unit": "J"}

Answer: 963.3397

Prompt: A body of mass 25.75 kg moves at 8.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 8.65^2 and multiply by 0.5 * 25.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.45 kg and a = 8.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 188.7725, "unit": "N"}

Answer: 188.7725

Prompt: A cart has mass 23.45 kg and measured acceleration 8.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.45 kg and a = 8.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 1.5671, "unit": "state_units"}

Answer: 1.5671

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=5, step size h=0.9, 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) = -0.15 y, so each step multiplies y by 1 - h*0.15.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 12346.0 / 1000.
Final: {"answer": 12.346, "unit": "kg"}

Answer: 12.346

Prompt: Convert 12346 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 12346.0 / 1000.


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

Answer: inconsistent

Prompt: In student derivation case 398689, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=91.9 V and R=192.8 ohm.
Final: {"answer": 43.805, "unit": "W"}

Answer: 43.805

Prompt: A resistor has resistance 192.8 ohm and voltage 91.9 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=91.9 V and R=192.8 ohm.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.9)=28.82 and f(19.5)=74.9.
3. The interval width is 9.6.
Final: {"answer": 497.856, "unit": "area_units"}

Answer: 497.856

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-18.7 from x=9.9 to x=19.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.9)=28.82 and f(19.5)=74.9.
The interval width is 9.6.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1010 mL to 1.01 L.
3. Compute M = 3.435 / 1.01.
Final: {"answer": 3.401, "unit": "mol/L"}

Answer: 3.401

Prompt: A solution contains 3.435 mol of solute in 1010 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1010 mL to 1.01 L.
Compute M = 3.435 / 1.01.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4408.5 / 100.
Final: {"answer": 44.085, "unit": "m"}

Answer: 44.085

Prompt: Convert 4408.5 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 4408.5 / 100.


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

Answer: inconsistent

Prompt: In quality-control check case 118439, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.24 and add it to the current value.
Final: {"answer": [0.576, 0.07, -1.054], "unit": "temperature_units"}

Answer: 0.576

Answer: 0.07

Answer: -1.054

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=-0.45, right=-1.5; current interior values are [1.2, 0.25, -1.45]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 1303.0 / 1000.
Final: {"answer": 1.303, "unit": "kg"}

Answer: 1.303

Prompt: Convert 1303 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 1303.0 / 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 lab notebook case 343175, 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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.4)=52.5 and f(-7)=44.8.
3. The interval width is 1.4.
Final: {"answer": 68.11, "unit": "area_units"}

Answer: 68.11

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+6.3 from x=-8.4 to x=-7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.4)=52.5 and f(-7)=44.8.
The interval width is 1.4.


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

Answer: consistent

Prompt: In quality-control check case 940097, 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. Use Newton's second law F = m a.
2. Substitute m = 0.7 kg and a = 1.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 0.875, "unit": "N"}

Answer: 0.875

Prompt: A cart has mass 0.7 kg and measured acceleration 1.25 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 = 0.7 kg and a = 1.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=104 degrees and keep the unit as newtons.
Final: {"answer": [-85.6404, 343.4847], "unit": "N"}

Answer: -85.6404

Answer: 343.4847

Prompt: A vector has magnitude 354 N at 104 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=104 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=281 mg, t=196 h, and T_half=80.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 51.9713, "unit": "mg"}

Answer: 51.9713

Prompt: A radioactive sample starts with 281 mg. Its half-life is 80.5 hours. How many mg remain after 196 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=281 mg, t=196 h, and T_half=80.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.4)=-7.34 and f(12)=-34.7.
3. The interval width is 7.6.
Final: {"answer": -159.752, "unit": "area_units"}

Answer: -159.752

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+8.5 from x=4.4 to x=12. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.4)=-7.34 and f(12)=-34.7.
The interval width is 7.6.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 24.15^2 and multiply by 0.5 * 17.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5176.0997, "unit": "J"}

Answer: 5176.0997

Prompt: A body of mass 17.75 kg moves at 24.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24.15^2 and multiply by 0.5 * 17.75.
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=370 mg, t=323.5 h, and T_half=101 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 40.1802, "unit": "mg"}

Answer: 40.1802

Prompt: A radioactive sample starts with 370 mg. Its half-life is 101 hours. How many mg remain after 323.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=370 mg, t=323.5 h, and T_half=101 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.1)=20.35 and f(8.8)=62.7.
3. The interval width is 7.7.
Final: {"answer": 319.7425, "unit": "area_units"}

Answer: 319.7425

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.5x+14.3 from x=1.1 to x=8.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.1)=20.35 and f(8.8)=62.7.
The interval width is 7.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [1.784, 1.446, 1.334], "unit": "temperature_units"}

Answer: 1.784

Answer: 1.446

Answer: 1.334

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=2.5, right=2.05; current interior values are [2.6, 0.15, 1.75]. Use r=0.32. 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=0.32 and add it to the current value.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.25 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 11.0025, "unit": "g"}

Answer: 11.0025

Prompt: A sample contains 0.25 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 = 0.25 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


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

```python
def pairwise_ratios_000556(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_000556"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_000556(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

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

try:
    pairwise_ratios_000556([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_000556([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.82 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 868.3519, "unit": "g"}

Answer: 868.3519

Prompt: A sample contains 4.82 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.82 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=296.5 mg, t=129 h, and T_half=109 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 130.5449, "unit": "mg"}

Answer: 130.5449

Prompt: A radioactive sample starts with 296.5 mg. Its half-life is 109 hours. How many mg remain after 129 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=296.5 mg, t=129 h, and T_half=109 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 140 * 2.135 * 43.
Final: {"answer": 12852.7, "unit": "J"}

Answer: 12852.7

Prompt: A 140 g sample has specific heat 2.135 J/(g*K). How much heat is needed to raise its temperature by 43 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 140 * 2.135 * 43.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.35 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 135.1175, "unit": "g"}

Answer: 135.1175

Prompt: A sample contains 1.35 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.35 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


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

```python
def clamp_000610(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_000610"}

Answer: python_code

Prompt: Write a Python function clamp_000610(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_000610(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4)=-5.6 and f(4.1)=-4.79.
3. The interval width is 8.1.
Final: {"answer": -42.0795, "unit": "area_units"}

Answer: -42.0795

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.1x+-5.2 from x=-4 to x=4.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4)=-5.6 and f(4.1)=-4.79.
The interval width is 8.1.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.
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 = -0.73 y with y(0)=70, step size h=1.35, 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) = -0.73 y, so each step multiplies y by 1 - h*0.73.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.62 y with y(0)=79.5, step size h=1.95, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=17 degrees through the sine of 2 theta.
3. Substitute v=63.4 m/s and g=9.81 m/s^2.
Final: {"answer": 229.1243, "unit": "m"}

Answer: 229.1243

Prompt: A projectile is launched on level ground with no air resistance at speed 63.4 m/s and angle 17 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=17 degrees through the sine of 2 theta.
Substitute v=63.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.2)=30.06 and f(11.4)=38.42.
3. The interval width is 2.2.
Final: {"answer": 75.328, "unit": "area_units"}

Answer: 75.328

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+-4.9 from x=9.2 to x=11.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.2)=30.06 and f(11.4)=38.42.
The interval width is 2.2.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.6 kg and a = 15.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 291.09, "unit": "N"}

Answer: 291.09

Prompt: A cart has mass 18.6 kg and measured acceleration 15.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.6 kg and a = 15.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=85.6 V and R=189.6 ohm.
Final: {"answer": 38.6464, "unit": "W"}

Answer: 38.6464

Prompt: A resistor has resistance 189.6 ohm and voltage 85.6 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=85.6 V and R=189.6 ohm.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=70 degrees through the sine of 2 theta.
3. Substitute v=23.9 m/s and g=9.81 m/s^2.
Final: {"answer": 37.4278, "unit": "m"}

Answer: 37.4278

Prompt: A projectile is launched on level ground with no air resistance at speed 23.9 m/s and angle 70 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=70 degrees through the sine of 2 theta.
Substitute v=23.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=100.1 V and R=80.3 ohm.
Final: {"answer": 124.7822, "unit": "W"}

Answer: 124.7822

Prompt: A resistor has resistance 80.3 ohm and voltage 100.1 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=100.1 V and R=80.3 ohm.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.54 * 8.314 * 440 / 48.0.
Final: {"answer": 41.1543, "unit": "kPa"}

Answer: 41.1543

Prompt: An ideal gas sample has n=0.54 mol, T=440 K, and V=48.0 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 = 0.54 * 8.314 * 440 / 48.0.


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_000772(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_000772"}

Answer: python_code

Prompt: Write a Python function center_values_000772(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_000772([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=147.5 mg, t=106.5 h, and T_half=94 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 67.2561, "unit": "mg"}

Answer: 67.2561

Prompt: A radioactive sample starts with 147.5 mg. Its half-life is 94 hours. How many mg remain after 106.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=147.5 mg, t=106.5 h, and T_half=94 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 = 3.81 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 222.6564, "unit": "g"}

Answer: 222.6564

Prompt: A sample contains 3.81 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.81 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 173.5 + 273.15.
Final: {"answer": 446.65, "unit": "K"}

Answer: 446.65

Prompt: Convert 173.5 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 173.5 + 273.15.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1595 * 3.265 * 87.
Final: {"answer": 453067.725, "unit": "J"}

Answer: 453067.725

Prompt: A 1595 g sample has specific heat 3.265 J/(g*K). How much heat is needed to raise its temperature by 87 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1595 * 3.265 * 87.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=319 degrees and keep the unit as newtons.
Final: {"answer": [208.2998, -181.0723], "unit": "N"}

Answer: 208.2998

Answer: -181.0723

Prompt: A vector has magnitude 276 N at 319 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=319 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In instrument manual case 467857, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.2 and interior values [1.6, 2.35, -1.85], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3624.5 / 100.
Final: {"answer": 36.245, "unit": "m"}

Answer: 36.245

Prompt: Convert 3624.5 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 3624.5 / 100.


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

Answer: consistent

Prompt: In field worksheet case 972866, 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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.9)=-23.22 and f(17.1)=-43.38.
3. The interval width is 7.2.
Final: {"answer": -239.76, "unit": "area_units"}

Answer: -239.76

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+4.5 from x=9.9 to x=17.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.9)=-23.22 and f(17.1)=-43.38.
The interval width is 7.2.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [1.132, 0.939, 1.306], "unit": "temperature_units"}

Answer: 1.132

Answer: 0.939

Answer: 1.306

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=2.3, right=0.6; current interior values are [-0.5, 1.5, 1.85]. Use r=0.34. Return the next interior vector.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 16.75^2 and multiply by 0.5 * 22.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3135.2859, "unit": "J"}

Answer: 3135.2859

Prompt: A body of mass 22.35 kg moves at 16.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.75^2 and multiply by 0.5 * 22.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.4)=7.32 and f(-3.3)=10.89.
3. The interval width is 5.1.
Final: {"answer": 46.4355, "unit": "area_units"}

Answer: 46.4355

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+13.2 from x=-8.4 to x=-3.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.4)=7.32 and f(-3.3)=10.89.
The interval width is 5.1.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1028.5 / 100.
Final: {"answer": 10.285, "unit": "m"}

Answer: 10.285

Prompt: Convert 1028.5 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 1028.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=22 degrees and keep the unit as newtons.
Final: {"answer": [295.7716, 119.4995], "unit": "N"}

Answer: 295.7716

Answer: 119.4995

Prompt: A vector has magnitude 319 N at 22 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=22 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": [-9.65, -22.75], "unit": "dimensionless"}

Answer: -9.65

Answer: -22.75

Prompt: A line passes through points (0.75, -29.9875) and (2.75, -49.2875). 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 14.2^2 and multiply by 0.5 * 23.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2409.598, "unit": "J"}

Answer: 2409.598

Prompt: A body of mass 23.9 kg moves at 14.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14.2^2 and multiply by 0.5 * 23.9.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.57 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 457.3976, "unit": "g"}

Answer: 457.3976

Prompt: A sample contains 4.57 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.57 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 425 mL to 0.425 L.
3. Compute M = 0.84 / 0.425.
Final: {"answer": 1.9765, "unit": "mol/L"}

Answer: 1.9765

Prompt: A solution contains 0.84 mol of solute in 425 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 425 mL to 0.425 L.
Compute M = 0.84 / 0.425.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=732.5 mg, t=14.5 h, and T_half=17 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 405.5522, "unit": "mg"}

Answer: 405.5522

Prompt: A radioactive sample starts with 732.5 mg. Its half-life is 17 hours. How many mg remain after 14.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=732.5 mg, t=14.5 h, and T_half=17 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 508 items and budget 51925, 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=270 degrees and keep the unit as newtons.
Final: {"answer": [0.0, -171.0], "unit": "N"}

Answer: 0.0

Answer: -171.0

Prompt: A vector has magnitude 171 N at 270 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=270 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.6 kg and a = 4.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 97.2, "unit": "N"}

Answer: 97.2

Prompt: A cart has mass 21.6 kg and measured acceleration 4.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.6 kg and a = 4.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=289.5 mg, t=51.5 h, and T_half=20.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 50.7461, "unit": "mg"}

Answer: 50.7461

Prompt: A radioactive sample starts with 289.5 mg. Its half-life is 20.5 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=289.5 mg, t=51.5 h, and T_half=20.5 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 = 8 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 467.52, "unit": "g"}

Answer: 467.52

Prompt: A sample contains 8 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 8 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=74 degrees and keep the unit as newtons.
Final: {"answer": [18.0542, 62.9626], "unit": "N"}

Answer: 18.0542

Answer: 62.9626

Prompt: A vector has magnitude 65.5 N at 74 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=74 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.65 kg and a = 8.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 113.295, "unit": "N"}

Answer: 113.295

Prompt: A cart has mass 13.65 kg and measured acceleration 8.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 13.65 kg and a = 8.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.81 * 8.314 * 561 / 30.0.
Final: {"answer": 436.8758, "unit": "kPa"}

Answer: 436.8758

Prompt: An ideal gas sample has n=2.81 mol, T=561 K, and V=30.0 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 = 2.81 * 8.314 * 561 / 30.0.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.3^2 and multiply by 0.5 * 29.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 27607.7552, "unit": "J"}

Answer: 27607.7552

Prompt: A body of mass 29.45 kg moves at 43.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.3^2 and multiply by 0.5 * 29.45.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.99 y with y(0)=42, step size h=1.1, 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) = -0.99 y, so each step multiplies y by 1 - h*0.99.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.7 kg and a = 9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 168.3, "unit": "N"}

Answer: 168.3

Prompt: A cart has mass 18.7 kg and measured acceleration 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 = 18.7 kg and a = 9 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [-0.722, 1.488, 1.018], "unit": "temperature_units"}

Answer: -0.722

Answer: 1.488

Answer: 1.018

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=1.25, right=2; current interior values are [-1.15, 1.8, 0.85]. Use r=0.08. Return the next interior vector.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.6, -14.25], "unit": "dimensionless"}

Answer: 8.6

Answer: -14.25

Prompt: A line passes through points (17.25, 134.1) and (22, 174.95). 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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.3)=-7.51 and f(-0.5)=-11.65.
3. The interval width is 1.8.
Final: {"answer": -17.244, "unit": "area_units"}

Answer: -17.244

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.3x+-12.8 from x=-2.3 to x=-0.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.3)=-7.51 and f(-0.5)=-11.65.
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=0.32 and add it to the current value.
Final: {"answer": [1.302, 1.11, 1.026], "unit": "temperature_units"}

Answer: 1.302

Answer: 1.11

Answer: 1.026

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=1.35, right=0.15; current interior values are [0.15, 2.55, 0.45]. Use r=0.32. 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=0.32 and add it to the current value.


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)=10 and h=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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 36.1^2 and multiply by 0.5 * 19.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 12510.816, "unit": "J"}

Answer: 12510.816

Prompt: A body of mass 19.2 kg moves at 36.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 36.1^2 and multiply by 0.5 * 19.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [3.4, 15.75], "unit": "dimensionless"}

Answer: 3.4

Answer: 15.75

Prompt: A line passes through points (0.25, 16.6) and (12.75, 59.1). 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. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=53.4 V and R=116.9 ohm.
Final: {"answer": 24.3932, "unit": "W"}

Answer: 24.3932

Prompt: A resistor has resistance 116.9 ohm and voltage 53.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=53.4 V and R=116.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=914 mg, t=21 h, and T_half=57 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 708.0117, "unit": "mg"}

Answer: 708.0117

Prompt: A radioactive sample starts with 914 mg. Its half-life is 57 hours. How many mg remain after 21 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=914 mg, t=21 h, and T_half=57 h.
The remaining amount has the same mass unit as the initial amount.


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.46 and interior values [1.35, 1.0, 2.55], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=11 degrees through the sine of 2 theta.
3. Substitute v=13.5 m/s and g=9.81 m/s^2.
Final: {"answer": 6.9594, "unit": "m"}

Answer: 6.9594

Prompt: A projectile is launched on level ground with no air resistance at speed 13.5 m/s and angle 11 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=11 degrees through the sine of 2 theta.
Substitute v=13.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.7 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1026.8892, "unit": "g"}

Answer: 1026.8892

Prompt: A sample contains 5.7 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 = 5.7 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.9)=30.93 and f(9.9)=54.43.
3. The interval width is 5.
Final: {"answer": 213.4, "unit": "area_units"}

Answer: 213.4

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+7.9 from x=4.9 to x=9.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.9)=30.93 and f(9.9)=54.43.
The interval width is 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=0.1 and add it to the current value.
Final: {"answer": [0.33, 0.095, -1.035], "unit": "temperature_units"}

Answer: 0.33

Answer: 0.095

Answer: -1.035

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=1.45, right=-0.6; current interior values are [0.2, 0.25, -1.25]. Use r=0.1. 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=0.1 and add it to the current value.


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=214.4 V and R=80.4 ohm.
Final: {"answer": 571.7333, "unit": "W"}

Answer: 571.7333

Prompt: A resistor has resistance 80.4 ohm and voltage 214.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=214.4 V and R=80.4 ohm.


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 8 steps and round the final state.
Final: {"answer": 15.6094, "unit": "state_units"}

Answer: 15.6094

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=44, step size h=1.35, 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
Apply that update for 8 steps and round the final state.


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=94.1 V and R=66.2 ohm.
Final: {"answer": 133.7585, "unit": "W"}

Answer: 133.7585

Prompt: A resistor has resistance 66.2 ohm and voltage 94.1 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=94.1 V and R=66.2 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.76 y, so each step multiplies y by 1 - h*0.76.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.76 y with y(0)=29.5, step size h=0.95, 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) = -0.76 y, so each step multiplies y by 1 - h*0.76.
Apply that update for 11 steps and round the final state.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each field crop record from batch 292762 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.55 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 999.8658, "unit": "g"}

Answer: 999.8658

Prompt: A sample contains 5.55 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.55 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


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

Answer: inconsistent

Prompt: In student derivation case 172619, 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. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 460 * 1.29 * 14.
Final: {"answer": 8307.6, "unit": "J"}

Answer: 8307.6

Prompt: A 460 g sample has specific heat 1.29 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 = 460 * 1.29 * 14.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 325 mL to 0.325 L.
3. Compute M = 4.86 / 0.325.
Final: {"answer": 14.9538, "unit": "mol/L"}

Answer: 14.9538

Prompt: A solution contains 4.86 mol of solute in 325 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 325 mL to 0.325 L.
Compute M = 4.86 / 0.325.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.9 kg and a = 8.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 145.885, "unit": "N"}

Answer: 145.885

Prompt: A cart has mass 17.9 kg and measured acceleration 8.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.9 kg and a = 8.15 m/s^2.
The unit kg*m/s^2 is one newton.


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=2.2 mol and T=297 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 = 17.1 kg and a = 2.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 35.91, "unit": "N"}

Answer: 35.91

Prompt: A cart has mass 17.1 kg and measured acceleration 2.1 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 = 17.1 kg and a = 2.1 m/s^2.
The unit kg*m/s^2 is one newton.


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_001240(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_001240"}

Answer: python_code

Prompt: Write a Python function finite_differences_001240(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_001240([5]) == []

assert finite_differences_001240([]) == []


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 85 * 2.985 * 44.
Final: {"answer": 11163.9, "unit": "J"}

Answer: 11163.9

Prompt: A 85 g sample has specific heat 2.985 J/(g*K). How much heat is needed to raise its temperature by 44 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 85 * 2.985 * 44.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=271 degrees and keep the unit as newtons.
Final: {"answer": [5.4452, -311.9525], "unit": "N"}

Answer: 5.4452

Answer: -311.9525

Prompt: A vector has magnitude 312 N at 271 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=271 degrees and keep the unit as newtons.


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 31.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 7.8^2 and multiply by 0.5 * 19.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 603.837, "unit": "J"}

Answer: 603.837

Prompt: A body of mass 19.85 kg moves at 7.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.8^2 and multiply by 0.5 * 19.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1775 * 3.23 * 62.
Final: {"answer": 355461.5, "unit": "J"}

Answer: 355461.5

Prompt: A 1775 g sample has specific heat 3.23 J/(g*K). How much heat is needed to raise its temperature by 62 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1775 * 3.23 * 62.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.8 kg and a = 15.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 245.69, "unit": "N"}

Answer: 245.69

Prompt: A cart has mass 15.8 kg and measured acceleration 15.55 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 = 15.8 kg and a = 15.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1805 * 1.725 * 53.
Final: {"answer": 165022.125, "unit": "J"}

Answer: 165022.125

Prompt: A 1805 g sample has specific heat 1.725 J/(g*K). How much heat is needed to raise its temperature by 53 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1805 * 1.725 * 53.


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

Answer: inconsistent

Prompt: In field worksheet case 454316, 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. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4650 mL to 4.65 L.
3. Compute M = 2.28 / 4.65.
Final: {"answer": 0.4903, "unit": "mol/L"}

Answer: 0.4903

Prompt: A solution contains 2.28 mol of solute in 4650 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4650 mL to 4.65 L.
Compute M = 2.28 / 4.65.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.24 and add it to the current value.
Final: {"answer": [0.688, 1.552, 1.252], "unit": "temperature_units"}

Answer: 0.688

Answer: 1.552

Answer: 1.252

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=0.45, right=-0.45; current interior values are [0.1, 2.2, 1.6]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. 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_001402(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_001402"}

Answer: python_code

Prompt: Write a Python function center_values_001402(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_001402([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.43 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 743.6464, "unit": "g"}

Answer: 743.6464

Prompt: A sample contains 7.43 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.43 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.9 * 8.314 * 252 / 81.7.
Final: {"answer": 23.0797, "unit": "kPa"}

Answer: 23.0797

Prompt: An ideal gas sample has n=0.9 mol, T=252 K, and V=81.7 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 = 0.9 * 8.314 * 252 / 81.7.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.4 kg and a = 9.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 59.52, "unit": "N"}

Answer: 59.52

Prompt: A cart has mass 6.4 kg and measured acceleration 9.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.4 kg and a = 9.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [1.13, 1.36, 1.8], "unit": "temperature_units"}

Answer: 1.13

Answer: 1.36

Answer: 1.8

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=2.25; current interior values are [2.45, 1.8, 0.15]. Use r=0.44. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.44 and add it to the current value.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-3.25, -21.25], "unit": "dimensionless"}

Answer: -3.25

Answer: -21.25

Prompt: A line passes through points (-14.75, 26.6875) and (-7.75, 3.9375). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=85.4 V and R=37.2 ohm.
Final: {"answer": 196.0527, "unit": "W"}

Answer: 196.0527

Prompt: A resistor has resistance 37.2 ohm and voltage 85.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=85.4 V and R=37.2 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.63 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 653.9663, "unit": "g"}

Answer: 653.9663

Prompt: A sample contains 3.63 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 = 3.63 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 54.1373, "unit": "state_units"}

Answer: 54.1373

Prompt: Use explicit Euler on dy/dt = -0.17 y with y(0)=77, step size h=0.95, 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) = -0.17 y, so each step multiplies y by 1 - h*0.17.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 0.65 kg and a = 1.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 0.845, "unit": "N"}

Answer: 0.845

Prompt: A cart has mass 0.65 kg and measured acceleration 1.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 0.65 kg and a = 1.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.35 * 8.314 * 488 / 106.4.
Final: {"answer": 89.6099, "unit": "kPa"}

Answer: 89.6099

Prompt: An ideal gas sample has n=2.35 mol, T=488 K, and V=106.4 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 = 2.35 * 8.314 * 488 / 106.4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=33.4 V and R=99 ohm.
Final: {"answer": 11.2683, "unit": "W"}

Answer: 11.2683

Prompt: A resistor has resistance 99 ohm and voltage 33.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=33.4 V and R=99 ohm.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=99 degrees and keep the unit as newtons.
Final: {"answer": [-17.8335, 112.5965], "unit": "N"}

Answer: -17.8335

Answer: 112.5965

Prompt: A vector has magnitude 114 N at 99 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=99 degrees and keep the unit as newtons.


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

```python
def threshold_flags_001510(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_001510"}

Answer: python_code

Prompt: Write a Python function threshold_flags_001510(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_001510([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_001510([], 5) == []

assert threshold_flags_001510([-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)=55 and h=0.4, 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. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=28.7 V and R=48.5 ohm.
Final: {"answer": 16.9833, "unit": "W"}

Answer: 16.9833

Prompt: A resistor has resistance 48.5 ohm and voltage 28.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=28.7 V and R=48.5 ohm.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.7, 29.25], "unit": "dimensionless"}

Answer: 7.7

Answer: 29.25

Prompt: A line passes through points (-18, -109.35) and (-16.5, -97.8). 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. 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 776138, 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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=968 mg, t=301 h, and T_half=24.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.1939, "unit": "mg"}

Answer: 0.1939

Prompt: A radioactive sample starts with 968 mg. Its half-life is 24.5 hours. How many mg remain after 301 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=968 mg, t=301 h, and T_half=24.5 h.
The remaining amount has the same mass unit as the initial amount.


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

Answer: inconsistent

Prompt: In model card equation case 890841, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.8, -1.75], "unit": "dimensionless"}

Answer: 4.8

Answer: -1.75

Prompt: A line passes through points (5.25, 23.45) and (13.5, 63.05). 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. Mass equals amount in moles times molar mass.
2. Use m = 3.77 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 220.3188, "unit": "g"}

Answer: 220.3188

Prompt: A sample contains 3.77 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.77 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2195 mL to 2.195 L.
3. Compute M = 3.23 / 2.195.
Final: {"answer": 1.4715, "unit": "mol/L"}

Answer: 1.4715

Prompt: A solution contains 3.23 mol of solute in 2195 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2195 mL to 2.195 L.
Compute M = 3.23 / 2.195.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.9)=9.81 and f(0.9)=-6.91.
3. The interval width is 8.8.
Final: {"answer": 12.76, "unit": "area_units"}

Answer: 12.76

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+-5.2 from x=-7.9 to x=0.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.9)=9.81 and f(0.9)=-6.91.
The interval width is 8.8.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In model card equation case 192485, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1655 * 3.875 * 76.
Final: {"answer": 487397.5, "unit": "J"}

Answer: 487397.5

Prompt: A 1655 g sample has specific heat 3.875 J/(g*K). How much heat is needed to raise its temperature by 76 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1655 * 3.875 * 76.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.24 * 8.314 * 318 / 45.8.
Final: {"answer": 71.5803, "unit": "kPa"}

Answer: 71.5803

Prompt: An ideal gas sample has n=1.24 mol, T=318 K, and V=45.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.24 * 8.314 * 318 / 45.8.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a routing scoring problem with 4169 items and budget 16580, 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 = 12.65 kg and a = 1.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 22.1375, "unit": "N"}

Answer: 22.1375

Prompt: A cart has mass 12.65 kg and measured acceleration 1.75 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 = 12.65 kg and a = 1.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=68 degrees through the sine of 2 theta.
3. Substitute v=71.6 m/s and g=9.81 m/s^2.
Final: {"answer": 363.0181, "unit": "m"}

Answer: 363.0181

Prompt: A projectile is launched on level ground with no air resistance at speed 71.6 m/s and angle 68 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=68 degrees through the sine of 2 theta.
Substitute v=71.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4270 mL to 4.27 L.
3. Compute M = 3.24 / 4.27.
Final: {"answer": 0.7588, "unit": "mol/L"}

Answer: 0.7588

Prompt: A solution contains 3.24 mol of solute in 4270 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4270 mL to 4.27 L.
Compute M = 3.24 / 4.27.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 16.35^2 and multiply by 0.5 * 25.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3381.6296, "unit": "J"}

Answer: 3381.6296

Prompt: A body of mass 25.3 kg moves at 16.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.35^2 and multiply by 0.5 * 25.3.
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=629 mg, t=359.5 h, and T_half=93 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 43.1511, "unit": "mg"}

Answer: 43.1511

Prompt: A radioactive sample starts with 629 mg. Its half-life is 93 hours. How many mg remain after 359.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=629 mg, t=359.5 h, and T_half=93 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 2336 items and budget 77505, 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -35.5 + 273.15.
Final: {"answer": 237.65, "unit": "K"}

Answer: 237.65

Prompt: Convert -35.5 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 -35.5 + 273.15.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 22.5^2 and multiply by 0.5 * 3.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 847.9688, "unit": "J"}

Answer: 847.9688

Prompt: A body of mass 3.35 kg moves at 22.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 22.5^2 and multiply by 0.5 * 3.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=34 V and R=89 ohm.
Final: {"answer": 12.9888, "unit": "W"}

Answer: 12.9888

Prompt: A resistor has resistance 89 ohm and voltage 34 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=34 V and R=89 ohm.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.05 kg and a = 6.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 21.1975, "unit": "N"}

Answer: 21.1975

Prompt: A cart has mass 3.05 kg and measured acceleration 6.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.05 kg and a = 6.95 m/s^2.
The unit kg*m/s^2 is one newton.