Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.8)=2.32 and f(6.1)=3.04.
3. The interval width is 0.3.
Final: {"answer": 0.804, "unit": "area_units"}

Answer: 0.804

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.4x+-11.6 from x=5.8 to x=6.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.8)=2.32 and f(6.1)=3.04.
The interval width is 0.3.


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=0.14 and add it to the current value.
Final: {"answer": [1.884, 0.284, -0.099], "unit": "temperature_units"}

Answer: 1.884

Answer: 0.284

Answer: -0.099

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.05, right=-0.3; current interior values are [2.85, -0.15, -0.05]. Use r=0.14. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.14 and add it to the current value.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.2, 19.0], "unit": "dimensionless"}

Answer: 2.2

Answer: 19.0

Prompt: A line passes through points (-17.5, -19.5) and (-7.75, 1.95). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 228146, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_004444(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_004444"}

Answer: python_code

Prompt: Write a Python function unit_vector_004444(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_004444(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: 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 3755 items and budget 585, 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=52 degrees through the sine of 2 theta.
3. Substitute v=26.7 m/s and g=9.81 m/s^2.
Final: {"answer": 70.5111, "unit": "m"}

Answer: 70.5111

Prompt: A projectile is launched on level ground with no air resistance at speed 26.7 m/s and angle 52 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=52 degrees through the sine of 2 theta.
Substitute v=26.7 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1700 * 1 * 42.
Final: {"answer": 71400.0, "unit": "J"}

Answer: 71400.0

Prompt: A 1700 g sample has specific heat 1 J/(g*K). How much heat is needed to raise its temperature by 42 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1700 * 1 * 42.


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=186.9 V and R=132.8 ohm.
Final: {"answer": 263.0392, "unit": "W"}

Answer: 263.0392

Prompt: A resistor has resistance 132.8 ohm and voltage 186.9 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=186.9 V and R=132.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=814 mg, t=5.5 h, and T_half=84 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 777.8827, "unit": "mg"}

Answer: 777.8827

Prompt: A radioactive sample starts with 814 mg. Its half-life is 84 hours. How many mg remain after 5.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=814 mg, t=5.5 h, and T_half=84 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 = 3.45 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 151.8345, "unit": "g"}

Answer: 151.8345

Prompt: A sample contains 3.45 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 = 3.45 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 3500 mL to 3.5 L.
3. Compute M = 1.015 / 3.5.
Final: {"answer": 0.29, "unit": "mol/L"}

Answer: 0.29

Prompt: A solution contains 1.015 mol of solute in 3500 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3500 mL to 3.5 L.
Compute M = 1.015 / 3.5.


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 12 steps and round the final state.
Final: {"answer": 0.1384, "unit": "state_units"}

Answer: 0.1384

Prompt: Use explicit Euler on dy/dt = -0.31 y with y(0)=67.5, step size h=1.3, 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) = -0.31 y, so each step multiplies y by 1 - h*0.31.
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(-3.7)=-28.01 and f(0.1)=-4.07.
3. The interval width is 3.8.
Final: {"answer": -60.952, "unit": "area_units"}

Answer: -60.952

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+-4.7 from x=-3.7 to x=0.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.7)=-28.01 and f(0.1)=-4.07.
The interval width is 3.8.

(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=0.36 and add it to the current value.
Final: {"answer": [1.668, 1.728, 0.658], "unit": "temperature_units"}

Answer: 1.668

Answer: 1.728

Answer: 0.658

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.9, right=-0.8; current interior values are [1.65, 0.45, 2.8]. Use r=0.36. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4318.0 / 100.
Final: {"answer": 43.18, "unit": "m"}

Answer: 43.18

Prompt: Convert 4318 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 4318.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=247 degrees and keep the unit as newtons.
Final: {"answer": [-146.3288, -344.7291], "unit": "N"}

Answer: -146.3288

Answer: -344.7291

Prompt: A vector has magnitude 374.5 N at 247 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=247 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.7, 7.5], "unit": "dimensionless"}

Answer: -2.7

Answer: 7.5

Prompt: A line passes through points (16.5, -37.05) and (25.75, -62.025). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In model card equation case 4077, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def normalize_004462(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_004462"}

Answer: python_code

Prompt: Write a Python function normalize_004462(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_004462([2, 3, 5]); assert len(out) == 3

try:
    normalize_004462([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: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=53.5 and h=0.6, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.55 kg and a = 15.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 285.67, "unit": "N"}

Answer: 285.67

Prompt: A cart has mass 18.55 kg and measured acceleration 15.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.55 kg and a = 15.4 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=71 degrees through the sine of 2 theta.
3. Substitute v=72 m/s and g=9.81 m/s^2.
Final: {"answer": 325.3404, "unit": "m"}

Answer: 325.3404

Prompt: A projectile is launched on level ground with no air resistance at speed 72 m/s and angle 71 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=71 degrees through the sine of 2 theta.
Substitute v=72 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 190 * 4.15 * 8.
Final: {"answer": 6308.0, "unit": "J"}

Answer: 6308.0

Prompt: A 190 g sample has specific heat 4.15 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 = 190 * 4.15 * 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=103.6 V and R=186.8 ohm.
Final: {"answer": 57.457, "unit": "W"}

Answer: 57.457

Prompt: A resistor has resistance 186.8 ohm and voltage 103.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=103.6 V and R=186.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=903 mg, t=24.5 h, and T_half=39 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 584.2237, "unit": "mg"}

Answer: 584.2237

Prompt: A radioactive sample starts with 903 mg. Its half-life is 39 hours. How many mg remain after 24.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=903 mg, t=24.5 h, and T_half=39 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.64 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 388.0416, "unit": "g"}

Answer: 388.0416

Prompt: A sample contains 6.64 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.64 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 4780 mL to 4.78 L.
3. Compute M = 3.59 / 4.78.
Final: {"answer": 0.751, "unit": "mol/L"}

Answer: 0.751

Prompt: A solution contains 3.59 mol of solute in 4780 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4780 mL to 4.78 L.
Compute M = 3.59 / 4.78.


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 4 steps and round the final state.
Final: {"answer": 26.9861, "unit": "state_units"}

Answer: 26.9861

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=57, step size h=1.55, 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) = -0.11 y, so each step multiplies y by 1 - h*0.11.
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(4.3)=33.97 and f(12.5)=82.35.
3. The interval width is 8.2.
Final: {"answer": 476.912, "unit": "area_units"}

Answer: 476.912

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.9x+8.6 from x=4.3 to x=12.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.3)=33.97 and f(12.5)=82.35.
The interval width is 8.2.


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=0.18 and add it to the current value.
Final: {"answer": [2.313, 2.372, 1.258], "unit": "temperature_units"}

Answer: 2.313

Answer: 2.372

Answer: 1.258

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=1.75; current interior values are [2.7, 2.75, 0.7]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -15.5 + 273.15.
Final: {"answer": 257.65, "unit": "K"}

Answer: 257.65

Prompt: Convert -15.5 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 -15.5 + 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=60 degrees and keep the unit as newtons.
Final: {"answer": [81.25, 140.7291], "unit": "N"}

Answer: 81.25

Answer: 140.7291

Prompt: A vector has magnitude 162.5 N at 60 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=60 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.4, 7.75], "unit": "dimensionless"}

Answer: 8.4

Answer: 7.75

Prompt: A line passes through points (-3.75, -23.75) and (7, 66.55). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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_004480(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_004480"}

Answer: python_code

Prompt: Write a Python function finite_differences_004480(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_004480([5]) == []

assert finite_differences_004480([]) == []


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 52.3 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 = 7.2 kg and a = 1.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 11.88, "unit": "N"}

Answer: 11.88

Prompt: A cart has mass 7.2 kg and measured acceleration 1.65 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 = 7.2 kg and a = 1.65 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=21 degrees through the sine of 2 theta.
3. Substitute v=75.2 m/s and g=9.81 m/s^2.
Final: {"answer": 385.7248, "unit": "m"}

Answer: 385.7248

Prompt: A projectile is launched on level ground with no air resistance at speed 75.2 m/s and angle 21 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=21 degrees through the sine of 2 theta.
Substitute v=75.2 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 = 5.34 * 8.314 * 267 / 40.9.
Final: {"answer": 289.8273, "unit": "kPa"}

Answer: 289.8273

Prompt: An ideal gas sample has n=5.34 mol, T=267 K, and V=40.9 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 = 5.34 * 8.314 * 267 / 40.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 575 * 0.675 * 66.
Final: {"answer": 25616.25, "unit": "J"}

Answer: 25616.25

Prompt: A 575 g sample has specific heat 0.675 J/(g*K). How much heat is needed to raise its temperature by 66 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 575 * 0.675 * 66.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=79 mg, t=291.5 h, and T_half=25.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0286, "unit": "mg"}

Answer: 0.0286

Prompt: A radioactive sample starts with 79 mg. Its half-life is 25.5 hours. How many mg remain after 291.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=79 mg, t=291.5 h, and T_half=25.5 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 = 7.18 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 315.9918, "unit": "g"}

Answer: 315.9918

Prompt: A sample contains 7.18 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 = 7.18 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 645 mL to 0.645 L.
3. Compute M = 0.985 / 0.645.
Final: {"answer": 1.5271, "unit": "mol/L"}

Answer: 1.5271

Prompt: A solution contains 0.985 mol of solute in 645 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 645 mL to 0.645 L.
Compute M = 0.985 / 0.645.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0003, "unit": "state_units"}

Answer: 0.0003

Prompt: Use explicit Euler on dy/dt = -0.69 y with y(0)=44, step size h=1.25, 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) = -0.69 y, so each step multiplies y by 1 - h*0.69.
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(6.3)=-0.77 and f(14.2)=7.92.
3. The interval width is 7.9.
Final: {"answer": 28.2425, "unit": "area_units"}

Answer: 28.2425

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.1x+-7.7 from x=6.3 to x=14.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.3)=-0.77 and f(14.2)=7.92.
The interval width is 7.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.24 and add it to the current value.
Final: {"answer": [1.204, 1.654, 0.978], "unit": "temperature_units"}

Answer: 1.204

Answer: 1.654

Answer: 0.978

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=2.8, right=-1.5; current interior values are [-0.2, 2.65, 1.35]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1041.0 / 100.
Final: {"answer": 10.41, "unit": "m"}

Answer: 10.41

Prompt: Convert 1041 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 1041.0 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.85, -13.25], "unit": "dimensionless"}

Answer: -6.85

Answer: -13.25

Prompt: A line passes through points (-9.25, 50.1125) and (-6, 27.85). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 560054, 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 threshold_flags_004498(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004498"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004498(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_004498([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004498([], 5) == []

assert threshold_flags_004498([-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 warehouse experiment records in release 284060, 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 = 20.45 kg and a = 12.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 251.535, "unit": "N"}

Answer: 251.535

Prompt: A cart has mass 20.45 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.45 kg and a = 12.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 30.25^2 and multiply by 0.5 * 29.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13634.4312, "unit": "J"}

Answer: 13634.4312

Prompt: A body of mass 29.8 kg moves at 30.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 30.25^2 and multiply by 0.5 * 29.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.48 * 8.314 * 539 / 71.4.
Final: {"answer": 30.126, "unit": "kPa"}

Answer: 30.126

Prompt: An ideal gas sample has n=0.48 mol, T=539 K, and V=71.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.48 * 8.314 * 539 / 71.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1450 * 1.465 * 14.
Final: {"answer": 29739.5, "unit": "J"}

Answer: 29739.5

Prompt: A 1450 g sample has specific heat 1.465 J/(g*K). How much heat is needed to raise its temperature by 14 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1450 * 1.465 * 14.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=168.6 V and R=173.2 ohm.
Final: {"answer": 164.1222, "unit": "W"}

Answer: 164.1222

Prompt: A resistor has resistance 173.2 ohm and voltage 168.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=168.6 V and R=173.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=764.5 mg, t=190.5 h, and T_half=37 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 21.5516, "unit": "mg"}

Answer: 21.5516

Prompt: A radioactive sample starts with 764.5 mg. Its half-life is 37 hours. How many mg remain after 190.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=764.5 mg, t=190.5 h, and T_half=37 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.33 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 190.5633, "unit": "g"}

Answer: 190.5633

Prompt: A sample contains 4.33 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.33 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) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=5, step size h=1.85, 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) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 12 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=0.42 and add it to the current value.
Final: {"answer": [0.65, 0.345, -1.048], "unit": "temperature_units"}

Answer: 0.65

Answer: 0.345

Answer: -1.048

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=2.95, right=-1.15; current interior values are [0.65, -1.65, 0.8]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 29688.0 / 1000.
Final: {"answer": 29.688, "unit": "kg"}

Answer: 29.688

Prompt: Convert 29688 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 29688.0 / 1000.


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

Answer: inconsistent

Prompt: In simulation spec case 223845, 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 normalize_004516(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_004516"}

Answer: python_code

Prompt: Write a Python function normalize_004516(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_004516([2, 3, 5]); assert len(out) == 3

try:
    normalize_004516([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: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each field survey record from batch 471846 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.55 kg and a = 1.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 20.6875, "unit": "N"}

Answer: 20.6875

Prompt: A cart has mass 16.55 kg and measured acceleration 1.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.55 kg and a = 1.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.15 * 8.314 * 258 / 94.3.
Final: {"answer": 26.1587, "unit": "kPa"}

Answer: 26.1587

Prompt: An ideal gas sample has n=1.15 mol, T=258 K, and V=94.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.15 * 8.314 * 258 / 94.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 145 * 3.53 * 15.
Final: {"answer": 7677.75, "unit": "J"}

Answer: 7677.75

Prompt: A 145 g sample has specific heat 3.53 J/(g*K). How much heat is needed to raise its temperature by 15 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 145 * 3.53 * 15.


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=66.2 V and R=14.7 ohm.
Final: {"answer": 298.1252, "unit": "W"}

Answer: 298.1252

Prompt: A resistor has resistance 14.7 ohm and voltage 66.2 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=66.2 V and R=14.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=145.5 mg, t=44 h, and T_half=71 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 94.6911, "unit": "mg"}

Answer: 94.6911

Prompt: A radioactive sample starts with 145.5 mg. Its half-life is 71 hours. How many mg remain after 44 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=145.5 mg, t=44 h, and T_half=71 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 1855 mL to 1.855 L.
3. Compute M = 0.865 / 1.855.
Final: {"answer": 0.4663, "unit": "mol/L"}

Answer: 0.4663

Prompt: A solution contains 0.865 mol of solute in 1855 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1855 mL to 1.855 L.
Compute M = 0.865 / 1.855.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.06 y, so each step multiplies y by 1 - h*0.06.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 6.3272, "unit": "state_units"}

Answer: 6.3272

Prompt: Use explicit Euler on dy/dt = -0.06 y with y(0)=7.5, step size h=0.4, 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) = -0.06 y, so each step multiplies y by 1 - h*0.06.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.6)=46.34 and f(9.9)=67.41.
3. The interval width is 4.3.
Final: {"answer": 244.5625, "unit": "area_units"}

Answer: 244.5625

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+18.9 from x=5.6 to x=9.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.6)=46.34 and f(9.9)=67.41.
The interval width is 4.3.


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=0.06 and add it to the current value.
Final: {"answer": [1.254, -0.307, 1.309], "unit": "temperature_units"}

Answer: 1.254

Answer: -0.307

Answer: 1.309

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=1.65, right=-1.1; current interior values are [1.35, -0.55, 1.6]. Use r=0.06. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 141.0 + 273.15.
Final: {"answer": 414.15, "unit": "K"}

Answer: 414.15

Prompt: Convert 141 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 141.0 + 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=21 degrees and keep the unit as newtons.
Final: {"answer": [253.4671, 97.2969], "unit": "N"}

Answer: 253.4671

Answer: 97.2969

Prompt: A vector has magnitude 271.5 N at 21 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=21 degrees and keep the unit as newtons.


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

```python
def normalize_004534(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_004534"}

Answer: python_code

Prompt: Write a Python function normalize_004534(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_004534([2, 3, 5]); assert len(out) == 3

try:
    normalize_004534([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=3.93 mol and T=291 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 = 9.35 kg and a = 8.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 82.7475, "unit": "N"}

Answer: 82.7475

Prompt: A cart has mass 9.35 kg and measured acceleration 8.85 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 = 9.35 kg and a = 8.85 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 = 6.35^2 and multiply by 0.5 * 19.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 387.096, "unit": "J"}

Answer: 387.096

Prompt: A body of mass 19.2 kg moves at 6.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.35^2 and multiply by 0.5 * 19.2.
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 = 4.49 * 8.314 * 387 / 8.8.
Final: {"answer": 1641.6654, "unit": "kPa"}

Answer: 1641.6654

Prompt: An ideal gas sample has n=4.49 mol, T=387 K, and V=8.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.49 * 8.314 * 387 / 8.8.


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=52.4 V and R=178.1 ohm.
Final: {"answer": 15.417, "unit": "W"}

Answer: 15.417

Prompt: A resistor has resistance 178.1 ohm and voltage 52.4 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=52.4 V and R=178.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=66.5 mg, t=179 h, and T_half=47 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 4.7462, "unit": "mg"}

Answer: 4.7462

Prompt: A radioactive sample starts with 66.5 mg. Its half-life is 47 hours. How many mg remain after 179 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=66.5 mg, t=179 h, and T_half=47 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 = 7.26 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 726.6316, "unit": "g"}

Answer: 726.6316

Prompt: A sample contains 7.26 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.26 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 8.1747, "unit": "state_units"}

Answer: 8.1747

Prompt: Use explicit Euler on dy/dt = -0.34 y with y(0)=43, step size h=1.25, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.
Apply that update for 3 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=0.26 and add it to the current value.
Final: {"answer": [2.184, 2.164, 1.122], "unit": "temperature_units"}

Answer: 2.184

Answer: 2.164

Answer: 1.122

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.15, right=-0.35; current interior values are [2.6, 2.45, 1.2]. 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 1726.0 / 1000.
Final: {"answer": 1.726, "unit": "kg"}

Answer: 1.726

Prompt: Convert 1726 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 1726.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=273 degrees and keep the unit as newtons.
Final: {"answer": [3.742, -71.402], "unit": "N"}

Answer: 3.742

Answer: -71.402

Prompt: A vector has magnitude 71.5 N at 273 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=273 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.15, 10.25], "unit": "dimensionless"}

Answer: -2.15

Answer: 10.25

Prompt: A line passes through points (8.5, -8.025) and (9.25, -9.6375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In field worksheet case 593625, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def threshold_flags_004552(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004552"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004552(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_004552([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004552([], 5) == []

assert threshold_flags_004552([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=18 and h=0.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.85 kg and a = 0.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 0.97, "unit": "N"}

Answer: 0.97

Prompt: A cart has mass 4.85 kg and measured acceleration 0.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.85 kg and a = 0.2 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 = 29.65^2 and multiply by 0.5 * 27.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 12043.9782, "unit": "J"}

Answer: 12043.9782

Prompt: A body of mass 27.4 kg moves at 29.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.65^2 and multiply by 0.5 * 27.4.
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=61 degrees through the sine of 2 theta.
3. Substitute v=48.1 m/s and g=9.81 m/s^2.
Final: {"answer": 200.0054, "unit": "m"}

Answer: 200.0054

Prompt: A projectile is launched on level ground with no air resistance at speed 48.1 m/s and angle 61 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=61 degrees through the sine of 2 theta.
Substitute v=48.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 555 * 2.44 * 74.
Final: {"answer": 100210.8, "unit": "J"}

Answer: 100210.8

Prompt: A 555 g sample has specific heat 2.44 J/(g*K). How much heat is needed to raise its temperature by 74 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 555 * 2.44 * 74.


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=17.9 V and R=126.5 ohm.
Final: {"answer": 2.5329, "unit": "W"}

Answer: 2.5329

Prompt: A resistor has resistance 126.5 ohm and voltage 17.9 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=17.9 V and R=126.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=806 mg, t=276.5 h, and T_half=10.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 806 mg. Its half-life is 10.5 hours. How many mg remain after 276.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=806 mg, t=276.5 h, and T_half=10.5 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 = 4.31 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 776.4724, "unit": "g"}

Answer: 776.4724

Prompt: A sample contains 4.31 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.31 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 3410 mL to 3.41 L.
3. Compute M = 3.43 / 3.41.
Final: {"answer": 1.0059, "unit": "mol/L"}

Answer: 1.0059

Prompt: A solution contains 3.43 mol of solute in 3410 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3410 mL to 3.41 L.
Compute M = 3.43 / 3.41.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.22 y, so each step multiplies y by 1 - h*0.22.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 21.4188, "unit": "state_units"}

Answer: 21.4188

Prompt: Use explicit Euler on dy/dt = -0.22 y with y(0)=59, step size h=0.4, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.22 y, so each step multiplies y by 1 - h*0.22.
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(5.3)=0.75 and f(13.6)=13.2.
3. The interval width is 8.3.
Final: {"answer": 57.8925, "unit": "area_units"}

Answer: 57.8925

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+-7.2 from x=5.3 to x=13.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.3)=0.75 and f(13.6)=13.2.
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=0.44 and add it to the current value.
Final: {"answer": [0.248, -0.796, -0.004], "unit": "temperature_units"}

Answer: 0.248

Answer: -0.796

Answer: -0.004

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=0.15, right=-0.45; current interior values are [-1.05, 0.7, -0.95]. Use r=0.44. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=306 degrees and keep the unit as newtons.
Final: {"answer": [217.7744, -299.7408], "unit": "N"}

Answer: 217.7744

Answer: -299.7408

Prompt: A vector has magnitude 370.5 N at 306 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=306 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.95, -25.25], "unit": "dimensionless"}

Answer: -7.95

Answer: -25.25

Prompt: A line passes through points (6, -72.95) and (12.25, -122.638). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In lab notebook case 559010, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. The 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_004570(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004570"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004570(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_004570([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004570([], 5) == []

assert threshold_flags_004570([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a routing scoring problem with 4634 items and budget 69250, 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 = 44.5^2 and multiply by 0.5 * 26.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 25941.275, "unit": "J"}

Answer: 25941.275

Prompt: A body of mass 26.2 kg moves at 44.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.5^2 and multiply by 0.5 * 26.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=61 degrees through the sine of 2 theta.
3. Substitute v=42.2 m/s and g=9.81 m/s^2.
Final: {"answer": 153.9488, "unit": "m"}

Answer: 153.9488

Prompt: A projectile is launched on level ground with no air resistance at speed 42.2 m/s and angle 61 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=61 degrees through the sine of 2 theta.
Substitute v=42.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 110 * 1.445 * 11.
Final: {"answer": 1748.45, "unit": "J"}

Answer: 1748.45

Prompt: A 110 g sample has specific heat 1.445 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 = 110 * 1.445 * 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=226.5 V and R=95.2 ohm.
Final: {"answer": 538.8892, "unit": "W"}

Answer: 538.8892

Prompt: A resistor has resistance 95.2 ohm and voltage 226.5 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=226.5 V and R=95.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=774 mg, t=72.5 h, and T_half=84 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 425.5234, "unit": "mg"}

Answer: 425.5234

Prompt: A radioactive sample starts with 774 mg. Its half-life is 84 hours. How many mg remain after 72.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=774 mg, t=72.5 h, and T_half=84 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.78 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 279.3432, "unit": "g"}

Answer: 279.3432

Prompt: A sample contains 4.78 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 = 4.78 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 1615 mL to 1.615 L.
3. Compute M = 3.075 / 1.615.
Final: {"answer": 1.904, "unit": "mol/L"}

Answer: 1.904

Prompt: A solution contains 3.075 mol of solute in 1615 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1615 mL to 1.615 L.
Compute M = 3.075 / 1.615.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 49.935, "unit": "state_units"}

Answer: 49.935

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=67.5, 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) = -0.03 y, so each step multiplies y by 1 - h*0.03.
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(-1.7)=-2.49 and f(2.1)=19.17.
3. The interval width is 3.8.
Final: {"answer": 31.692, "unit": "area_units"}

Answer: 31.692

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.7x+7.2 from x=-1.7 to x=2.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.7)=-2.49 and f(2.1)=19.17.
The interval width is 3.8.


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=0.06 and add it to the current value.
Final: {"answer": [-0.575, -1.68, 1.043], "unit": "temperature_units"}

Answer: -0.575

Answer: -1.68

Answer: 1.043

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=1; current interior values are [-0.65, -1.95, 1.25]. Use r=0.06. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=272 degrees and keep the unit as newtons.
Final: {"answer": [3.2631, -93.443], "unit": "N"}

Answer: 3.2631

Answer: -93.443

Prompt: A vector has magnitude 93.5 N at 272 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=272 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.6, -14.5], "unit": "dimensionless"}

Answer: 7.6

Answer: -14.5

Prompt: A line passes through points (-17.75, -149.4) and (-3, -37.3). 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=11.5 and h=0.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.35 kg and a = 7.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 189.93, "unit": "N"}

Answer: 189.93

Prompt: A cart has mass 24.35 kg and measured acceleration 7.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.35 kg and a = 7.8 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 = 17.25^2 and multiply by 0.5 * 25.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3860.8734, "unit": "J"}

Answer: 3860.8734

Prompt: A body of mass 25.95 kg moves at 17.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.25^2 and multiply by 0.5 * 25.95.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=30 degrees through the sine of 2 theta.
3. Substitute v=38.7 m/s and g=9.81 m/s^2.
Final: {"answer": 132.2159, "unit": "m"}

Answer: 132.2159

Prompt: A projectile is launched on level ground with no air resistance at speed 38.7 m/s and angle 30 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=30 degrees through the sine of 2 theta.
Substitute v=38.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.05 * 8.314 * 593 / 98.2.
Final: {"answer": 253.5389, "unit": "kPa"}

Answer: 253.5389

Prompt: An ideal gas sample has n=5.05 mol, T=593 K, and V=98.2 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 = 5.05 * 8.314 * 593 / 98.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 535 * 3.84 * 43.
Final: {"answer": 88339.2, "unit": "J"}

Answer: 88339.2

Prompt: A 535 g sample has specific heat 3.84 J/(g*K). How much heat is needed to raise its temperature by 43 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 535 * 3.84 * 43.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=728.5 mg, t=188.5 h, and T_half=51.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 57.6237, "unit": "mg"}

Answer: 57.6237

Prompt: A radioactive sample starts with 728.5 mg. Its half-life is 51.5 hours. How many mg remain after 188.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=728.5 mg, t=188.5 h, and T_half=51.5 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 = 4.18 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 418.3637, "unit": "g"}

Answer: 418.3637

Prompt: A sample contains 4.18 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.18 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 3805 mL to 3.805 L.
3. Compute M = 4.185 / 3.805.
Final: {"answer": 1.0999, "unit": "mol/L"}

Answer: 1.0999

Prompt: A solution contains 4.185 mol of solute in 3805 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3805 mL to 3.805 L.
Compute M = 4.185 / 3.805.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.69 y with y(0)=47.5, step size h=1.3, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.5)=-63.8 and f(12.5)=-86.6.
3. The interval width is 3.
Final: {"answer": -225.6, "unit": "area_units"}

Answer: -225.6

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.6x+8.4 from x=9.5 to x=12.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.5)=-63.8 and f(12.5)=-86.6.
The interval width is 3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [0.948, 0.238, -0.06], "unit": "temperature_units"}

Answer: 0.948

Answer: 0.238

Answer: -0.06

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.95, right=-1.95; current interior values are [1.3, 0.15, 0.1]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 37133.0 / 1000.
Final: {"answer": 37.133, "unit": "kg"}

Answer: 37.133

Prompt: Convert 37133 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 37133.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=97 degrees and keep the unit as newtons.
Final: {"answer": [-55.6334, 453.0973], "unit": "N"}

Answer: -55.6334

Answer: 453.0973

Prompt: A vector has magnitude 456.5 N at 97 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=97 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.2, 26.5], "unit": "dimensionless"}

Answer: -6.2

Answer: 26.5

Prompt: A line passes through points (8.25, -24.65) and (22.5, -113). 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 pairwise_ratios_004606(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_004606"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_004606(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

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

try:
    pairwise_ratios_004606([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_004606([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=0.12 and interior values [-1.8, 1.0, -0.2], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 39.8^2 and multiply by 0.5 * 20.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 15840.4, "unit": "J"}

Answer: 15840.4

Prompt: A body of mass 20 kg moves at 39.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 39.8^2 and multiply by 0.5 * 20.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=48 degrees through the sine of 2 theta.
3. Substitute v=48 m/s and g=9.81 m/s^2.
Final: {"answer": 233.5758, "unit": "m"}

Answer: 233.5758

Prompt: A projectile is launched on level ground with no air resistance at speed 48 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=48 degrees through the sine of 2 theta.
Substitute v=48 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 = 3.58 * 8.314 * 548 / 84.5.
Final: {"answer": 193.0265, "unit": "kPa"}

Answer: 193.0265

Prompt: An ideal gas sample has n=3.58 mol, T=548 K, and V=84.5 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 = 3.58 * 8.314 * 548 / 84.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 450 * 3.875 * 79.
Final: {"answer": 137756.25, "unit": "J"}

Answer: 137756.25

Prompt: A 450 g sample has specific heat 3.875 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 = 450 * 3.875 * 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=15.5 V and R=154.2 ohm.
Final: {"answer": 1.558, "unit": "W"}

Answer: 1.558

Prompt: A resistor has resistance 154.2 ohm and voltage 15.5 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=15.5 V and R=154.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=624.5 mg, t=76.5 h, and T_half=10 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 3.1092, "unit": "mg"}

Answer: 3.1092

Prompt: A radioactive sample starts with 624.5 mg. Its half-life is 10 hours. How many mg remain after 76.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=624.5 mg, t=76.5 h, and T_half=10 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.95 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 495.4307, "unit": "g"}

Answer: 495.4307

Prompt: A sample contains 4.95 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.95 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 1415 mL to 1.415 L.
3. Compute M = 3.05 / 1.415.
Final: {"answer": 2.1555, "unit": "mol/L"}

Answer: 2.1555

Prompt: A solution contains 3.05 mol of solute in 1415 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1415 mL to 1.415 L.
Compute M = 3.05 / 1.415.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 14.3983, "unit": "state_units"}

Answer: 14.3983

Prompt: Use explicit Euler on dy/dt = -0.42 y with y(0)=25, step size h=0.4, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.5)=51.65 and f(15.5)=83.45.
3. The interval width is 6.
Final: {"answer": 405.3, "unit": "area_units"}

Answer: 405.3

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.3x+1.3 from x=9.5 to x=15.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.5)=51.65 and f(15.5)=83.45.
The interval width is 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=0.24 and add it to the current value.
Final: {"answer": [-0.228, 0.024, 0.496], "unit": "temperature_units"}

Answer: -0.228

Answer: 0.024

Answer: 0.496

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=1.65, right=-0.75; current interior values are [-1.2, 0.0, 1.3]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 3464.0 / 1000.
Final: {"answer": 3.464, "unit": "kg"}

Answer: 3.464

Prompt: Convert 3464 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 3464.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=142 degrees and keep the unit as newtons.
Final: {"answer": [-287.2299, 224.4086], "unit": "N"}

Answer: -287.2299

Answer: 224.4086

Prompt: A vector has magnitude 364.5 N at 142 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=142 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": [5.85, 28.25], "unit": "dimensionless"}

Answer: 5.85

Answer: 28.25

Prompt: A line passes through points (13, 104.3) and (22.5, 159.875). 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. density times acceleration times height gives kg/(m*s^2), or pascal
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 409723, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_004624(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_004624"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_004624(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

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

try:
    pairwise_ratios_004624([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_004624([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.8 kg and a = 11.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 120.96, "unit": "N"}

Answer: 120.96

Prompt: A cart has mass 10.8 kg and measured acceleration 11.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.8 kg and a = 11.2 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 = 44.65^2 and multiply by 0.5 * 27.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 27163.1066, "unit": "J"}

Answer: 27163.1066

Prompt: A body of mass 27.25 kg moves at 44.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.65^2 and multiply by 0.5 * 27.25.
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 = 4.18 * 8.314 * 557 / 15.5.
Final: {"answer": 1248.8486, "unit": "kPa"}

Answer: 1248.8486

Prompt: An ideal gas sample has n=4.18 mol, T=557 K, and V=15.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.18 * 8.314 * 557 / 15.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 835 * 2.89 * 5.
Final: {"answer": 12065.75, "unit": "J"}

Answer: 12065.75

Prompt: A 835 g sample has specific heat 2.89 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 835 * 2.89 * 5.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=581.5 mg, t=247 h, and T_half=41 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 8.9336, "unit": "mg"}

Answer: 8.9336

Prompt: A radioactive sample starts with 581.5 mg. Its half-life is 41 hours. How many mg remain after 247 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=581.5 mg, t=247 h, and T_half=41 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.8 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 46.752, "unit": "g"}

Answer: 46.752

Prompt: A sample contains 0.8 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.8 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 3025 mL to 3.025 L.
3. Compute M = 0.325 / 3.025.
Final: {"answer": 0.1074, "unit": "mol/L"}

Answer: 0.1074

Prompt: A solution contains 0.325 mol of solute in 3025 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3025 mL to 3.025 L.
Compute M = 0.325 / 3.025.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.81 y with y(0)=78, step size h=1.45, 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) = -0.81 y, so each step multiplies y by 1 - h*0.81.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1394.0 / 100.
Final: {"answer": 13.94, "unit": "m"}

Answer: 13.94

Prompt: Convert 1394 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 1394.0 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-3.8, 27.25], "unit": "dimensionless"}

Answer: -3.8

Answer: 27.25

Prompt: A line passes through points (-12.25, 73.8) and (-10.25, 66.2). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In quality-control check case 326065, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def clamp_004642(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_004642"}

Answer: python_code

Prompt: Write a Python function clamp_004642(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_004642(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile survey record from batch 929960 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.6 kg and a = 9.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 160.19, "unit": "N"}

Answer: 160.19

Prompt: A cart has mass 16.6 kg and measured acceleration 9.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.6 kg and a = 9.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.95^2 and multiply by 0.5 * 26.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5333.2335, "unit": "J"}

Answer: 5333.2335

Prompt: A body of mass 26.8 kg moves at 19.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.95^2 and multiply by 0.5 * 26.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=31 degrees through the sine of 2 theta.
3. Substitute v=60.9 m/s and g=9.81 m/s^2.
Final: {"answer": 333.8109, "unit": "m"}

Answer: 333.8109

Prompt: A projectile is launched on level ground with no air resistance at speed 60.9 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=31 degrees through the sine of 2 theta.
Substitute v=60.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.84 * 8.314 * 268 / 79.2.
Final: {"answer": 51.7651, "unit": "kPa"}

Answer: 51.7651

Prompt: An ideal gas sample has n=1.84 mol, T=268 K, and V=79.2 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 = 1.84 * 8.314 * 268 / 79.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 615 * 2.035 * 27.
Final: {"answer": 33791.175, "unit": "J"}

Answer: 33791.175

Prompt: A 615 g sample has specific heat 2.035 J/(g*K). How much heat is needed to raise its temperature by 27 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 615 * 2.035 * 27.


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=22.2 V and R=178.2 ohm.
Final: {"answer": 2.7657, "unit": "W"}

Answer: 2.7657

Prompt: A resistor has resistance 178.2 ohm and voltage 22.2 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=22.2 V and R=178.2 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3310 mL to 3.31 L.
3. Compute M = 1.25 / 3.31.
Final: {"answer": 0.3776, "unit": "mol/L"}

Answer: 0.3776

Prompt: A solution contains 1.25 mol of solute in 3310 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3310 mL to 3.31 L.
Compute M = 1.25 / 3.31.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=19, step size h=1.05, 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) = -0.85 y, so each step multiplies y by 1 - h*0.85.
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(6)=34.3 and f(13.4)=62.42.
3. The interval width is 7.4.
Final: {"answer": 357.864, "unit": "area_units"}

Answer: 357.864

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+11.5 from x=6 to x=13.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6)=34.3 and f(13.4)=62.42.
The interval width is 7.4.