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_007594(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_007594"}

Answer: python_code

Prompt: Write a Python function center_values_007594(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_007594([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.05 kg and a = 5.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 123.48, "unit": "N"}

Answer: 123.48

Prompt: A cart has mass 22.05 kg and measured acceleration 5.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.05 kg and a = 5.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 36.5^2 and multiply by 0.5 * 26.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 17885.4562, "unit": "J"}

Answer: 17885.4562

Prompt: A body of mass 26.85 kg moves at 36.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 36.5^2 and multiply by 0.5 * 26.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.57 * 8.314 * 615 / 96.0.
Final: {"answer": 136.8822, "unit": "kPa"}

Answer: 136.8822

Prompt: An ideal gas sample has n=2.57 mol, T=615 K, and V=96.0 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 = 2.57 * 8.314 * 615 / 96.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 845 * 4.195 * 79.
Final: {"answer": 280037.225, "unit": "J"}

Answer: 280037.225

Prompt: A 845 g sample has specific heat 4.195 J/(g*K). How much heat is needed to raise its temperature by 79 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 845 * 4.195 * 79.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=8.3 V and R=1.9 ohm.
Final: {"answer": 36.2579, "unit": "W"}

Answer: 36.2579

Prompt: A resistor has resistance 1.9 ohm and voltage 8.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=8.3 V and R=1.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=423 mg, t=19 h, and T_half=35.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 291.8944, "unit": "mg"}

Answer: 291.8944

Prompt: A radioactive sample starts with 423 mg. Its half-life is 35.5 hours. How many mg remain after 19 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=423 mg, t=19 h, and T_half=35.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.23 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 54.1323, "unit": "g"}

Answer: 54.1323

Prompt: A sample contains 1.23 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 = 1.23 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1525 mL to 1.525 L.
3. Compute M = 0.99 / 1.525.
Final: {"answer": 0.6492, "unit": "mol/L"}

Answer: 0.6492

Prompt: A solution contains 0.99 mol of solute in 1525 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1525 mL to 1.525 L.
Compute M = 0.99 / 1.525.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.0034, "unit": "state_units"}

Answer: 0.0034

Prompt: Use explicit Euler on dy/dt = -0.64 y with y(0)=16.5, step size h=1.75, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.8)=58 and f(-3.9)=39.15.
3. The interval width is 2.9.
Final: {"answer": 140.8675, "unit": "area_units"}

Answer: 140.8675

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.5x+13.8 from x=-6.8 to x=-3.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.8)=58 and f(-3.9)=39.15.
The interval width is 2.9.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.2 and add it to the current value.
Final: {"answer": [1.66, 1.92, 2.0], "unit": "temperature_units"}

Answer: 1.66

Answer: 1.92

Answer: 2.0

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.45; current interior values are [2.55, 1.45, 2.7]. Use r=0.2. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=320 degrees and keep the unit as newtons.
Final: {"answer": [291.0969, -244.2593], "unit": "N"}

Answer: 291.0969

Answer: -244.2593

Prompt: A vector has magnitude 380 N at 320 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=320 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.95, 0.25], "unit": "dimensionless"}

Answer: 1.95

Answer: 0.25

Prompt: A line passes through points (-19.75, -38.2625) and (-5.75, -10.9625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 368017, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
import math

def unit_vector_007612(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_007612"}

Answer: python_code

Prompt: Write a Python function unit_vector_007612(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_007612(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid registry invoice records in release 933485, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.8^2 and multiply by 0.5 * 16.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3283.335, "unit": "J"}

Answer: 3283.335

Prompt: A body of mass 16.75 kg moves at 19.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.8^2 and multiply by 0.5 * 16.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=25 degrees through the sine of 2 theta.
3. Substitute v=49.9 m/s and g=9.81 m/s^2.
Final: {"answer": 194.4402, "unit": "m"}

Answer: 194.4402

Prompt: A projectile is launched on level ground with no air resistance at speed 49.9 m/s and angle 25 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=25 degrees through the sine of 2 theta.
Substitute v=49.9 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 = 2.17 * 8.314 * 615 / 53.0.
Final: {"answer": 209.3481, "unit": "kPa"}

Answer: 209.3481

Prompt: An ideal gas sample has n=2.17 mol, T=615 K, and V=53.0 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 = 2.17 * 8.314 * 615 / 53.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1275 * 4.03 * 16.
Final: {"answer": 82212.0, "unit": "J"}

Answer: 82212.0

Prompt: A 1275 g sample has specific heat 4.03 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1275 * 4.03 * 16.


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=108.8 V and R=156.4 ohm.
Final: {"answer": 75.687, "unit": "W"}

Answer: 75.687

Prompt: A resistor has resistance 156.4 ohm and voltage 108.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=108.8 V and R=156.4 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.14 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 138.1914, "unit": "g"}

Answer: 138.1914

Prompt: A sample contains 3.14 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.14 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3030 mL to 3.03 L.
3. Compute M = 0.15 / 3.03.
Final: {"answer": 0.0495, "unit": "mol/L"}

Answer: 0.0495

Prompt: A solution contains 0.15 mol of solute in 3030 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3030 mL to 3.03 L.
Compute M = 0.15 / 3.03.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.1 y, so each step multiplies y by 1 - h*0.1.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 27.4054, "unit": "state_units"}

Answer: 27.4054

Prompt: Use explicit Euler on dy/dt = -0.1 y with y(0)=34.5, step size h=0.45, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.1 y, so each step multiplies y by 1 - h*0.1.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.7)=-22.13 and f(2.6)=18.54.
3. The interval width is 8.3.
Final: {"answer": -14.8985, "unit": "area_units"}

Answer: -14.8985

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+5.8 from x=-5.7 to x=2.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.7)=-22.13 and f(2.6)=18.54.
The interval width is 8.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [1.358, 0.724, 1.155], "unit": "temperature_units"}

Answer: 1.358

Answer: 0.724

Answer: 1.155

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=2.5; current interior values are [2.45, -0.55, 1.35]. Use r=0.26. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 29647.0 / 1000.
Final: {"answer": 29.647, "unit": "kg"}

Answer: 29.647

Prompt: Convert 29647 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 29647.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=277 degrees and keep the unit as newtons.
Final: {"answer": [21.3881, -174.1918], "unit": "N"}

Answer: 21.3881

Answer: -174.1918

Prompt: A vector has magnitude 175.5 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.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.2, 11.0], "unit": "dimensionless"}

Answer: -1.2

Answer: 11.0

Prompt: A line passes through points (18.75, -11.5) and (25.25, -19.3). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def threshold_flags_007630(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_007630"}

Answer: python_code

Prompt: Write a Python function threshold_flags_007630(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_007630([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_007630([], 5) == []

assert threshold_flags_007630([-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: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid field clinical records in release 614339, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.9 kg and a = 2.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 42.25, "unit": "N"}

Answer: 42.25

Prompt: A cart has mass 16.9 kg and measured acceleration 2.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.9 kg and a = 2.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 24.6^2 and multiply by 0.5 * 7.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2269.35, "unit": "J"}

Answer: 2269.35

Prompt: A body of mass 7.5 kg moves at 24.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24.6^2 and multiply by 0.5 * 7.5.
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 = 1.9 * 8.314 * 310 / 107.2.
Final: {"answer": 45.6805, "unit": "kPa"}

Answer: 45.6805

Prompt: An ideal gas sample has n=1.9 mol, T=310 K, and V=107.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.9 * 8.314 * 310 / 107.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 555 * 3.79 * 75.
Final: {"answer": 157758.75, "unit": "J"}

Answer: 157758.75

Prompt: A 555 g sample has specific heat 3.79 J/(g*K). How much heat is needed to raise its temperature by 75 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 555 * 3.79 * 75.


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=18.2 V and R=153.4 ohm.
Final: {"answer": 2.1593, "unit": "W"}

Answer: 2.1593

Prompt: A resistor has resistance 153.4 ohm and voltage 18.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=18.2 V and R=153.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=34.5 mg, t=283.5 h, and T_half=33 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0895, "unit": "mg"}

Answer: 0.0895

Prompt: A radioactive sample starts with 34.5 mg. Its half-life is 33 hours. How many mg remain after 283.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=34.5 mg, t=283.5 h, and T_half=33 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 = 7.38 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1329.5513, "unit": "g"}

Answer: 1329.5513

Prompt: A sample contains 7.38 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 = 7.38 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3055 mL to 3.055 L.
3. Compute M = 3.545 / 3.055.
Final: {"answer": 1.1604, "unit": "mol/L"}

Answer: 1.1604

Prompt: A solution contains 3.545 mol of solute in 3055 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3055 mL to 3.055 L.
Compute M = 3.545 / 3.055.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0013, "unit": "state_units"}

Answer: 0.0013

Prompt: Use explicit Euler on dy/dt = -0.6 y with y(0)=79.5, step size h=1, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.1)=-57.35 and f(7.4)=-67.1.
3. The interval width is 1.3.
Final: {"answer": -80.8925, "unit": "area_units"}

Answer: -80.8925

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.5x+-11.6 from x=6.1 to x=7.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.1)=-57.35 and f(7.4)=-67.1.
The interval width is 1.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.18 and add it to the current value.
Final: {"answer": [-0.102, 2.118, 1.886], "unit": "temperature_units"}

Answer: -0.102

Answer: 2.118

Answer: 1.886

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=-0.9, right=0.9; current interior values are [-0.75, 3.0, 1.85]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1407.0 / 100.
Final: {"answer": 14.07, "unit": "m"}

Answer: 14.07

Prompt: Convert 1407 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 1407.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=88 degrees and keep the unit as newtons.
Final: {"answer": [4.694, 134.4181], "unit": "N"}

Answer: 4.694

Answer: 134.4181

Prompt: A vector has magnitude 134.5 N at 88 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=88 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In simulation spec case 976397, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_007648(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007648"}

Answer: python_code

Prompt: Write a Python function running_total_007648(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 13.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.35 kg and a = 14.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 47.235, "unit": "N"}

Answer: 47.235

Prompt: A cart has mass 3.35 kg and measured acceleration 14.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.35 kg and a = 14.1 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=55 degrees through the sine of 2 theta.
3. Substitute v=11.5 m/s and g=9.81 m/s^2.
Final: {"answer": 12.6681, "unit": "m"}

Answer: 12.6681

Prompt: A projectile is launched on level ground with no air resistance at speed 11.5 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=11.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.51 * 8.314 * 537 / 97.6.
Final: {"answer": 114.8175, "unit": "kPa"}

Answer: 114.8175

Prompt: An ideal gas sample has n=2.51 mol, T=537 K, and V=97.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.51 * 8.314 * 537 / 97.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1845 * 2.115 * 81.
Final: {"answer": 316076.175, "unit": "J"}

Answer: 316076.175

Prompt: A 1845 g sample has specific heat 2.115 J/(g*K). How much heat is needed to raise its temperature by 81 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1845 * 2.115 * 81.


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=179.1 V and R=83.6 ohm.
Final: {"answer": 383.6939, "unit": "W"}

Answer: 383.6939

Prompt: A resistor has resistance 83.6 ohm and voltage 179.1 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=179.1 V and R=83.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=25.5 mg, t=49 h, and T_half=74.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 16.1639, "unit": "mg"}

Answer: 16.1639

Prompt: A radioactive sample starts with 25.5 mg. Its half-life is 74.5 hours. How many mg remain after 49 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=25.5 mg, t=49 h, and T_half=74.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.76 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 102.8544, "unit": "g"}

Answer: 102.8544

Prompt: A sample contains 1.76 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 = 1.76 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 4090 mL to 4.09 L.
3. Compute M = 0.925 / 4.09.
Final: {"answer": 0.2262, "unit": "mol/L"}

Answer: 0.2262

Prompt: A solution contains 0.925 mol of solute in 4090 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4090 mL to 4.09 L.
Compute M = 0.925 / 4.09.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 10.141, "unit": "state_units"}

Answer: 10.141

Prompt: Use explicit Euler on dy/dt = -0.36 y with y(0)=60.5, step size h=0.5, 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) = -0.36 y, so each step multiplies y by 1 - h*0.36.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.6)=-5.26 and f(5.1)=20.64.
3. The interval width is 3.5.
Final: {"answer": 26.915, "unit": "area_units"}

Answer: 26.915

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.4x+-17.1 from x=1.6 to x=5.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.6)=-5.26 and f(5.1)=20.64.
The interval width is 3.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [-0.547, -0.646, -0.163], "unit": "temperature_units"}

Answer: -0.547

Answer: -0.646

Answer: -0.163

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=-1.9, right=0.1; current interior values are [0.3, -1.35, 0.2]. Use r=0.22. 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=0.22 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -44.0 + 273.15.
Final: {"answer": 229.15, "unit": "K"}

Answer: 229.15

Prompt: Convert -44 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 -44.0 + 273.15.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.95, 6.0], "unit": "dimensionless"}

Answer: -9.95

Answer: 6.0

Prompt: A line passes through points (-2, 25.9) and (1.25, -6.4375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In student derivation case 796349, 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 Newton's second law F = m a.
2. Substitute m = 4.85 kg and a = 15.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 77.3575, "unit": "N"}

Answer: 77.3575

Prompt: A cart has mass 4.85 kg and measured acceleration 15.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.85 kg and a = 15.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 15.95^2 and multiply by 0.5 * 8.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1125.7311, "unit": "J"}

Answer: 1125.7311

Prompt: A body of mass 8.85 kg moves at 15.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.95^2 and multiply by 0.5 * 8.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=34 degrees through the sine of 2 theta.
3. Substitute v=62.8 m/s and g=9.81 m/s^2.
Final: {"answer": 372.7487, "unit": "m"}

Answer: 372.7487

Prompt: A projectile is launched on level ground with no air resistance at speed 62.8 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=34 degrees through the sine of 2 theta.
Substitute v=62.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.53 * 8.314 * 260 / 105.5.
Final: {"answer": 51.8384, "unit": "kPa"}

Answer: 51.8384

Prompt: An ideal gas sample has n=2.53 mol, T=260 K, and V=105.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.53 * 8.314 * 260 / 105.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1200 * 1.42 * 60.
Final: {"answer": 102240.0, "unit": "J"}

Answer: 102240.0

Prompt: A 1200 g sample has specific heat 1.42 J/(g*K). How much heat is needed to raise its temperature by 60 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1200 * 1.42 * 60.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=64.4 V and R=62 ohm.
Final: {"answer": 66.8929, "unit": "W"}

Answer: 66.8929

Prompt: A resistor has resistance 62 ohm and voltage 64.4 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=64.4 V and R=62 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.35 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 42.3353, "unit": "g"}

Answer: 42.3353

Prompt: A sample contains 2.35 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.35 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2425 mL to 2.425 L.
3. Compute M = 2.005 / 2.425.
Final: {"answer": 0.8268, "unit": "mol/L"}

Answer: 0.8268

Prompt: A solution contains 2.005 mol of solute in 2425 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2425 mL to 2.425 L.
Compute M = 2.005 / 2.425.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 47.0739, "unit": "state_units"}

Answer: 47.0739

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=72.5, step size h=0.35, 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) = -0.11 y, so each step multiplies y by 1 - h*0.11.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [1.502, 1.742, -0.494], "unit": "temperature_units"}

Answer: 1.502

Answer: 1.742

Answer: -0.494

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.6, right=-1.5; current interior values are [2.15, 0.35, 1.45]. Use r=0.48. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.48 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 32878.0 / 1000.
Final: {"answer": 32.878, "unit": "kg"}

Answer: 32.878

Prompt: Convert 32878 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 32878.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.0, 15.5], "unit": "dimensionless"}

Answer: -5.0

Answer: 15.5

Prompt: A line passes through points (13.5, -52) and (17.5, -72). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In student derivation case 897591, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def center_values_007684(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_007684"}

Answer: python_code

Prompt: Write a Python function center_values_007684(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_007684([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid warehouse invoice records in release 416289, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.5 kg and a = 12.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 208.725, "unit": "N"}

Answer: 208.725

Prompt: A cart has mass 16.5 kg and measured acceleration 12.65 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 = 16.5 kg and a = 12.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 40.65^2 and multiply by 0.5 * 7.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6031.3421, "unit": "J"}

Answer: 6031.3421

Prompt: A body of mass 7.3 kg moves at 40.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 40.65^2 and multiply by 0.5 * 7.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=58 degrees through the sine of 2 theta.
3. Substitute v=68.2 m/s and g=9.81 m/s^2.
Final: {"answer": 426.1475, "unit": "m"}

Answer: 426.1475

Prompt: A projectile is launched on level ground with no air resistance at speed 68.2 m/s and angle 58 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=58 degrees through the sine of 2 theta.
Substitute v=68.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.86 * 8.314 * 587 / 107.5.
Final: {"answer": 84.4409, "unit": "kPa"}

Answer: 84.4409

Prompt: An ideal gas sample has n=1.86 mol, T=587 K, and V=107.5 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 = 1.86 * 8.314 * 587 / 107.5.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=733.5 mg, t=175 h, and T_half=98 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 212.7387, "unit": "mg"}

Answer: 212.7387

Prompt: A radioactive sample starts with 733.5 mg. Its half-life is 98 hours. How many mg remain after 175 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=733.5 mg, t=175 h, and T_half=98 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3980 mL to 3.98 L.
3. Compute M = 4.585 / 3.98.
Final: {"answer": 1.152, "unit": "mol/L"}

Answer: 1.152

Prompt: A solution contains 4.585 mol of solute in 3980 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3980 mL to 3.98 L.
Compute M = 4.585 / 3.98.


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 5 steps and round the final state.
Final: {"answer": 6.321, "unit": "state_units"}

Answer: 6.321

Prompt: Use explicit Euler on dy/dt = -0.17 y with y(0)=14.5, step size h=0.9, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.16 and add it to the current value.
Final: {"answer": [-0.912, -0.702, 0.474], "unit": "temperature_units"}

Answer: -0.912

Answer: -0.702

Answer: 0.474

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-0.55; current interior values are [-1.4, -0.95, 1.05]. Use r=0.16. 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=0.16 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 47969.0 / 1000.
Final: {"answer": 47.969, "unit": "kg"}

Answer: 47.969

Prompt: Convert 47969 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 47969.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=263 degrees and keep the unit as newtons.
Final: {"answer": [-34.6109, -281.8831], "unit": "N"}

Answer: -34.6109

Answer: -281.8831

Prompt: A vector has magnitude 284 N at 263 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=263 degrees and keep the unit as newtons.


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 quality-control check case 142122, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
coulomb per second is ampere
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

```python
def center_values_007702(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_007702"}

Answer: python_code

Prompt: Write a Python function center_values_007702(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_007702([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid laboratory clinical records in release 800003, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=10 degrees through the sine of 2 theta.
3. Substitute v=77.6 m/s and g=9.81 m/s^2.
Final: {"answer": 209.9453, "unit": "m"}

Answer: 209.9453

Prompt: A projectile is launched on level ground with no air resistance at speed 77.6 m/s and angle 10 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=10 degrees through the sine of 2 theta.
Substitute v=77.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.84 * 8.314 * 481 / 50.9.
Final: {"answer": 380.2618, "unit": "kPa"}

Answer: 380.2618

Prompt: An ideal gas sample has n=4.84 mol, T=481 K, and V=50.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.84 * 8.314 * 481 / 50.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1115 * 1.625 * 118.
Final: {"answer": 213801.25, "unit": "J"}

Answer: 213801.25

Prompt: A 1115 g sample has specific heat 1.625 J/(g*K). How much heat is needed to raise its temperature by 118 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1115 * 1.625 * 118.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=193.9 V and R=175.7 ohm.
Final: {"answer": 213.9853, "unit": "W"}

Answer: 213.9853

Prompt: A resistor has resistance 175.7 ohm and voltage 193.9 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=193.9 V and R=175.7 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.49 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 989.0564, "unit": "g"}

Answer: 989.0564

Prompt: A sample contains 5.49 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 = 5.49 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 240 mL to 0.24 L.
3. Compute M = 1.555 / 0.24.
Final: {"answer": 6.4792, "unit": "mol/L"}

Answer: 6.4792

Prompt: A solution contains 1.555 mol of solute in 240 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 240 mL to 0.24 L.
Compute M = 1.555 / 0.24.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 8.9493, "unit": "state_units"}

Answer: 8.9493

Prompt: Use explicit Euler on dy/dt = -0.4 y with y(0)=54.5, step size h=0.65, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.7)=22.34 and f(16.5)=44.1.
3. The interval width is 6.8.
Final: {"answer": 225.896, "unit": "area_units"}

Answer: 225.896

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.2x+-8.7 from x=9.7 to x=16.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.7)=22.34 and f(16.5)=44.1.
The interval width is 6.8.


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=0.08 and add it to the current value.
Final: {"answer": [1.268, 2.39, -0.626], "unit": "temperature_units"}

Answer: 1.268

Answer: 2.39

Answer: -0.626

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=0.35; current interior values are [1.0, 2.85, -1.05]. 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": [-3.65, 11.75], "unit": "dimensionless"}

Answer: -3.65

Answer: 11.75

Prompt: A line passes through points (2, 4.45) and (4.25, -3.7625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 573589, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_007720(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_007720"}

Answer: python_code

Prompt: Write a Python function finite_differences_007720(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_007720([5]) == []

assert finite_differences_007720([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a scheduler scoring problem with 3843 items and budget 27545, 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 38.6^2 and multiply by 0.5 * 23.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 17134.54, "unit": "J"}

Answer: 17134.54

Prompt: A body of mass 23 kg moves at 38.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 38.6^2 and multiply by 0.5 * 23.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=43 degrees through the sine of 2 theta.
3. Substitute v=9.7 m/s and g=9.81 m/s^2.
Final: {"answer": 9.5679, "unit": "m"}

Answer: 9.5679

Prompt: A projectile is launched on level ground with no air resistance at speed 9.7 m/s and angle 43 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=43 degrees through the sine of 2 theta.
Substitute v=9.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.69 * 8.314 * 544 / 59.8.
Final: {"answer": 203.4511, "unit": "kPa"}

Answer: 203.4511

Prompt: An ideal gas sample has n=2.69 mol, T=544 K, and V=59.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.69 * 8.314 * 544 / 59.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 465 * 1.355 * 119.
Final: {"answer": 74978.925, "unit": "J"}

Answer: 74978.925

Prompt: A 465 g sample has specific heat 1.355 J/(g*K). How much heat is needed to raise its temperature by 119 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 465 * 1.355 * 119.


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=230.3 V and R=130.3 ohm.
Final: {"answer": 407.046, "unit": "W"}

Answer: 407.046

Prompt: A resistor has resistance 130.3 ohm and voltage 230.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=230.3 V and R=130.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=166.5 mg, t=62.5 h, and T_half=79.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 96.5507, "unit": "mg"}

Answer: 96.5507

Prompt: A radioactive sample starts with 166.5 mg. Its half-life is 79.5 hours. How many mg remain after 62.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=166.5 mg, t=62.5 h, and T_half=79.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.41 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 18.0441, "unit": "g"}

Answer: 18.0441

Prompt: A sample contains 0.41 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 = 0.41 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 3.4877, "unit": "state_units"}

Answer: 3.4877

Prompt: Use explicit Euler on dy/dt = -0.39 y with y(0)=6, step size h=0.15, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.5)=26.25 and f(10)=51.
3. The interval width is 7.5.
Final: {"answer": 289.6875, "unit": "area_units"}

Answer: 289.6875

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+18 from x=2.5 to x=10. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.5)=26.25 and f(10)=51.
The interval width is 7.5.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 31235.0 / 1000.
Final: {"answer": 31.235, "unit": "kg"}

Answer: 31.235

Prompt: Convert 31235 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 31235.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=114 degrees and keep the unit as newtons.
Final: {"answer": [-21.3537, 47.9611], "unit": "N"}

Answer: -21.3537

Answer: 47.9611

Prompt: A vector has magnitude 52.5 N at 114 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=114 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.3, 7.0], "unit": "dimensionless"}

Answer: -5.3

Answer: 7.0

Prompt: A line passes through points (-10.75, 63.975) and (-1.25, 13.625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 892293, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def weighted_sum_007738(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_007738"}

Answer: python_code

Prompt: Write a Python function weighted_sum_007738(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_007738([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a routing scoring problem with 2751 items and budget 96720, 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.25^2 and multiply by 0.5 * 19.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6804.4922, "unit": "J"}

Answer: 6804.4922

Prompt: A body of mass 19.75 kg moves at 26.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.25^2 and multiply by 0.5 * 19.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.37 * 8.314 * 505 / 107.6.
Final: {"answer": 53.4576, "unit": "kPa"}

Answer: 53.4576

Prompt: An ideal gas sample has n=1.37 mol, T=505 K, and V=107.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.37 * 8.314 * 505 / 107.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 595 * 3.005 * 11.
Final: {"answer": 19667.725, "unit": "J"}

Answer: 19667.725

Prompt: A 595 g sample has specific heat 3.005 J/(g*K). How much heat is needed to raise its temperature by 11 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 595 * 3.005 * 11.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=133.8 V and R=119.5 ohm.
Final: {"answer": 149.8112, "unit": "W"}

Answer: 149.8112

Prompt: A resistor has resistance 119.5 ohm and voltage 133.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=133.8 V and R=119.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=915 mg, t=161.5 h, and T_half=66.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 169.9606, "unit": "mg"}

Answer: 169.9606

Prompt: A radioactive sample starts with 915 mg. Its half-life is 66.5 hours. How many mg remain after 161.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=915 mg, t=161.5 h, and T_half=66.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.25 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 189.93, "unit": "g"}

Answer: 189.93

Prompt: A sample contains 3.25 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 = 3.25 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 1495 mL to 1.495 L.
3. Compute M = 4.96 / 1.495.
Final: {"answer": 3.3177, "unit": "mol/L"}

Answer: 3.3177

Prompt: A solution contains 4.96 mol of solute in 1495 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1495 mL to 1.495 L.
Compute M = 4.96 / 1.495.


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": [0.968, 2.156, 1.054], "unit": "temperature_units"}

Answer: 0.968

Answer: 2.156

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=1.3, right=0.8; current interior values are [0.8, 2.4, 0.95]. Use r=0.08. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 152.5 + 273.15.
Final: {"answer": 425.65, "unit": "K"}

Answer: 425.65

Prompt: Convert 152.5 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 152.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=235 degrees and keep the unit as newtons.
Final: {"answer": [-29.2524, -41.7768], "unit": "N"}

Answer: -29.2524

Answer: -41.7768

Prompt: A vector has magnitude 51 N at 235 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=235 degrees and keep the unit as newtons.


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

Answer: inconsistent

Prompt: In sensor calibration case 691242, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def normalize_007756(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_007756"}

Answer: python_code

Prompt: Write a Python function normalize_007756(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_007756([2, 3, 5]); assert len(out) == 3

try:
    normalize_007756([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=0.82 mol and T=378 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 = 16.1 kg and a = 14.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 239.89, "unit": "N"}

Answer: 239.89

Prompt: A cart has mass 16.1 kg and measured acceleration 14.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.1 kg and a = 14.9 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 25.35^2 and multiply by 0.5 * 4.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1413.7695, "unit": "J"}

Answer: 1413.7695

Prompt: A body of mass 4.4 kg moves at 25.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.35^2 and multiply by 0.5 * 4.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=12 degrees through the sine of 2 theta.
3. Substitute v=51 m/s and g=9.81 m/s^2.
Final: {"answer": 107.8412, "unit": "m"}

Answer: 107.8412

Prompt: A projectile is launched on level ground with no air resistance at speed 51 m/s and angle 12 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=12 degrees through the sine of 2 theta.
Substitute v=51 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.71 * 8.314 * 434 / 48.0.
Final: {"answer": 278.8897, "unit": "kPa"}

Answer: 278.8897

Prompt: An ideal gas sample has n=3.71 mol, T=434 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 = 3.71 * 8.314 * 434 / 48.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 365 * 4.555 * 8.
Final: {"answer": 13300.6, "unit": "J"}

Answer: 13300.6

Prompt: A 365 g sample has specific heat 4.555 J/(g*K). How much heat is needed to raise its temperature by 8 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 365 * 4.555 * 8.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=188.1 V and R=143.1 ohm.
Final: {"answer": 247.2509, "unit": "W"}

Answer: 247.2509

Prompt: A resistor has resistance 143.1 ohm and voltage 188.1 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=188.1 V and R=143.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=780.5 mg, t=266 h, and T_half=49.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 18.8242, "unit": "mg"}

Answer: 18.8242

Prompt: A radioactive sample starts with 780.5 mg. Its half-life is 49.5 hours. How many mg remain after 266 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=780.5 mg, t=266 h, and T_half=49.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.97 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 174.7197, "unit": "g"}

Answer: 174.7197

Prompt: A sample contains 3.97 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.97 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2645 mL to 2.645 L.
3. Compute M = 2.07 / 2.645.
Final: {"answer": 0.7826, "unit": "mol/L"}

Answer: 0.7826

Prompt: A solution contains 2.07 mol of solute in 2645 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2645 mL to 2.645 L.
Compute M = 2.07 / 2.645.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.84 y, so each step multiplies y by 1 - h*0.84.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 7.8736, "unit": "state_units"}

Answer: 7.8736

Prompt: Use explicit Euler on dy/dt = -0.84 y with y(0)=41, step size h=0.25, 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) = -0.84 y, so each step multiplies y by 1 - h*0.84.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.9)=76.8 and f(-7.3)=61.2.
3. The interval width is 2.6.
Final: {"answer": 179.4, "unit": "area_units"}

Answer: 179.4

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+17.4 from x=-9.9 to x=-7.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.9)=76.8 and f(-7.3)=61.2.
The interval width is 2.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [1.153, 1.935, 0.902], "unit": "temperature_units"}

Answer: 1.153

Answer: 1.935

Answer: 0.902

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=0.5, right=-0.95; current interior values are [1.4, 1.65, 2.65]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 85.0 + 273.15.
Final: {"answer": 358.15, "unit": "K"}

Answer: 358.15

Prompt: Convert 85 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 85.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=117 degrees and keep the unit as newtons.
Final: {"answer": [-68.3256, 134.0965], "unit": "N"}

Answer: -68.3256

Answer: 134.0965

Prompt: A vector has magnitude 150.5 N at 117 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=117 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": [0.55, -29.0], "unit": "dimensionless"}

Answer: 0.55

Answer: -29.0

Prompt: A line passes through points (8.25, -24.4625) and (20, -18). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In student derivation case 610843, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def safe_mean_007774(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_007774"}

Answer: python_code

Prompt: Write a Python function safe_mean_007774(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_007774([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.16 and interior values [-1.7, 0.2, 1.6], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.75 kg and a = 4.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 7.875, "unit": "N"}

Answer: 7.875

Prompt: A cart has mass 1.75 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 = 1.75 kg and a = 4.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 8^2 and multiply by 0.5 * 16.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 513.6, "unit": "J"}

Answer: 513.6

Prompt: A body of mass 16.05 kg moves at 8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 8^2 and multiply by 0.5 * 16.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=83 degrees through the sine of 2 theta.
3. Substitute v=83.9 m/s and g=9.81 m/s^2.
Final: {"answer": 173.5922, "unit": "m"}

Answer: 173.5922

Prompt: A projectile is launched on level ground with no air resistance at speed 83.9 m/s and angle 83 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=83 degrees through the sine of 2 theta.
Substitute v=83.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.4 * 8.314 * 502 / 67.9.
Final: {"answer": 331.9233, "unit": "kPa"}

Answer: 331.9233

Prompt: An ideal gas sample has n=5.4 mol, T=502 K, and V=67.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.4 * 8.314 * 502 / 67.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 530 * 1.38 * 2.
Final: {"answer": 1462.8, "unit": "J"}

Answer: 1462.8

Prompt: A 530 g sample has specific heat 1.38 J/(g*K). How much heat is needed to raise its temperature by 2 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 530 * 1.38 * 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=156.8 V and R=26.4 ohm.
Final: {"answer": 931.297, "unit": "W"}

Answer: 931.297

Prompt: A resistor has resistance 26.4 ohm and voltage 156.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=156.8 V and R=26.4 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.88 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 188.1636, "unit": "g"}

Answer: 188.1636

Prompt: A sample contains 1.88 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 = 1.88 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 1900 mL to 1.9 L.
3. Compute M = 1.005 / 1.9.
Final: {"answer": 0.5289, "unit": "mol/L"}

Answer: 0.5289

Prompt: A solution contains 1.005 mol of solute in 1900 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1900 mL to 1.9 L.
Compute M = 1.005 / 1.9.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 5.0758, "unit": "state_units"}

Answer: 5.0758

Prompt: Use explicit Euler on dy/dt = -0.31 y with y(0)=26.5, step size h=0.45, 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) = -0.31 y, so each step multiplies y by 1 - h*0.31.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.6)=-31.18 and f(12.5)=-65.4.
3. The interval width is 5.9.
Final: {"answer": -284.911, "unit": "area_units"}

Answer: -284.911

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+7.1 from x=6.6 to x=12.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.6)=-31.18 and f(12.5)=-65.4.
The interval width is 5.9.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1826.5 / 100.
Final: {"answer": 18.265, "unit": "m"}

Answer: 18.265

Prompt: Convert 1826.5 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 1826.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=18 degrees and keep the unit as newtons.
Final: {"answer": [356.6462, 115.8814], "unit": "N"}

Answer: 356.6462

Answer: 115.8814

Prompt: A vector has magnitude 375 N at 18 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=18 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.35, -26.5], "unit": "dimensionless"}

Answer: -4.35

Answer: -26.5

Prompt: A line passes through points (-12.75, 28.9625) and (-8, 8.3). 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. 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 lab notebook case 307487, 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 Newton's second law F = m a.
2. Substitute m = 4.5 kg and a = 4.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 21.825, "unit": "N"}

Answer: 21.825

Prompt: A cart has mass 4.5 kg and measured acceleration 4.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.5 kg and a = 4.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 22.6^2 and multiply by 0.5 * 13.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3332.709, "unit": "J"}

Answer: 3332.709

Prompt: A body of mass 13.05 kg moves at 22.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 22.6^2 and multiply by 0.5 * 13.05.
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 = 4.12 * 8.314 * 360 / 71.2.
Final: {"answer": 173.1928, "unit": "kPa"}

Answer: 173.1928

Prompt: An ideal gas sample has n=4.12 mol, T=360 K, and V=71.2 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 = 4.12 * 8.314 * 360 / 71.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 590 * 1.995 * 32.
Final: {"answer": 37665.6, "unit": "J"}

Answer: 37665.6

Prompt: A 590 g sample has specific heat 1.995 J/(g*K). How much heat is needed to raise its temperature by 32 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 590 * 1.995 * 32.


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=180.5 V and R=120.6 ohm.
Final: {"answer": 270.1513, "unit": "W"}

Answer: 270.1513

Prompt: A resistor has resistance 120.6 ohm and voltage 180.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=180.5 V and R=120.6 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.62 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 29.1843, "unit": "g"}

Answer: 29.1843

Prompt: A sample contains 1.62 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.62 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 640 mL to 0.64 L.
3. Compute M = 4.2 / 0.64.
Final: {"answer": 6.5625, "unit": "mol/L"}

Answer: 6.5625

Prompt: A solution contains 4.2 mol of solute in 640 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 640 mL to 0.64 L.
Compute M = 4.2 / 0.64.


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 5 steps and round the final state.
Final: {"answer": 6.3416, "unit": "state_units"}

Answer: 6.3416

Prompt: Use explicit Euler on dy/dt = -0.17 y with y(0)=47.5, step size h=1.95, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.2)=26.08 and f(-3.4)=19.36.
3. The interval width is 2.8.
Final: {"answer": 63.616, "unit": "area_units"}

Answer: 63.616

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.4x+11.2 from x=-6.2 to x=-3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.2)=26.08 and f(-3.4)=19.36.
The interval width is 2.8.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22364.0 / 1000.
Final: {"answer": 22.364, "unit": "kg"}

Answer: 22.364

Prompt: Convert 22364 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 22364.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=94 degrees and keep the unit as newtons.
Final: {"answer": [-5.5805, 79.8051], "unit": "N"}

Answer: -5.5805

Answer: 79.8051

Prompt: A vector has magnitude 80 N at 94 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=94 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.9, 27.75], "unit": "dimensionless"}

Answer: -1.9

Answer: 27.75

Prompt: A line passes through points (-4.5, 36.3) and (8.5, 11.6). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def finite_differences_007810(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_007810"}

Answer: python_code

Prompt: Write a Python function finite_differences_007810(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_007810([5]) == []

assert finite_differences_007810([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=0.38 mol and T=520 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=69 degrees through the sine of 2 theta.
3. Substitute v=69.5 m/s and g=9.81 m/s^2.
Final: {"answer": 329.4667, "unit": "m"}

Answer: 329.4667

Prompt: A projectile is launched on level ground with no air resistance at speed 69.5 m/s and angle 69 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=69 degrees through the sine of 2 theta.
Substitute v=69.5 m/s and g=9.81 m/s^2.