Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=291.5 mg, t=12 h, and T_half=12.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 149.8476, "unit": "mg"}

Answer: 149.8476

Prompt: A radioactive sample starts with 291.5 mg. Its half-life is 12.5 hours. How many mg remain after 12 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=291.5 mg, t=12 h, and T_half=12.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.25 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 55.0125, "unit": "g"}

Answer: 55.0125

Prompt: A sample contains 1.25 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.25 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 1035 mL to 1.035 L.
3. Compute M = 2.7 / 1.035.
Final: {"answer": 2.6087, "unit": "mol/L"}

Answer: 2.6087

Prompt: A solution contains 2.7 mol of solute in 1035 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1035 mL to 1.035 L.
Compute M = 2.7 / 1.035.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.78 y with y(0)=19.5, step size h=1.25, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3)=25.1 and f(10.4)=55.44.
3. The interval width is 7.4.
Final: {"answer": 297.998, "unit": "area_units"}

Answer: 297.998

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+12.8 from x=3 to x=10.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3)=25.1 and f(10.4)=55.44.
The interval width is 7.4.

(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=0.3 and add it to the current value.
Final: {"answer": [1.475, 1.42, 0.395], "unit": "temperature_units"}

Answer: 1.475

Answer: 1.42

Answer: 0.395

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=0.3; current interior values are [2.6, 2.35, -1.0]. Use r=0.3. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 357.5 / 100.
Final: {"answer": 3.575, "unit": "m"}

Answer: 3.575

Prompt: Convert 357.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 357.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=258 degrees and keep the unit as newtons.
Final: {"answer": [-45.8445, -215.6815], "unit": "N"}

Answer: -45.8445

Answer: -215.6815

Prompt: A vector has magnitude 220.5 N at 258 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=258 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 function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def safe_mean_006046(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_006046"}

Answer: python_code

Prompt: Write a Python function safe_mean_006046(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_006046([])
    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)=80 and h=0.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.2 kg and a = 2.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 17.64, "unit": "N"}

Answer: 17.64

Prompt: A cart has mass 7.2 kg and measured acceleration 2.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.2 kg and a = 2.45 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=6 degrees through the sine of 2 theta.
3. Substitute v=75.9 m/s and g=9.81 m/s^2.
Final: {"answer": 122.0938, "unit": "m"}

Answer: 122.0938

Prompt: A projectile is launched on level ground with no air resistance at speed 75.9 m/s and angle 6 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=6 degrees through the sine of 2 theta.
Substitute v=75.9 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.56 * 8.314 * 240 / 43.1.
Final: {"answer": 118.5179, "unit": "kPa"}

Answer: 118.5179

Prompt: An ideal gas sample has n=2.56 mol, T=240 K, and V=43.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.56 * 8.314 * 240 / 43.1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=110.8 V and R=100 ohm.
Final: {"answer": 122.7664, "unit": "W"}

Answer: 122.7664

Prompt: A resistor has resistance 100 ohm and voltage 110.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=110.8 V and R=100 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=310 mg, t=325 h, and T_half=0.5 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 310 mg. Its half-life is 0.5 hours. How many mg remain after 325 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=310 mg, t=325 h, and T_half=0.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.25 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 112.5938, "unit": "g"}

Answer: 112.5938

Prompt: A sample contains 6.25 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.25 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2355 mL to 2.355 L.
3. Compute M = 4.24 / 2.355.
Final: {"answer": 1.8004, "unit": "mol/L"}

Answer: 1.8004

Prompt: A solution contains 4.24 mol of solute in 2355 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2355 mL to 2.355 L.
Compute M = 4.24 / 2.355.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": -0.6465, "unit": "state_units"}

Answer: -0.6465

Prompt: Use explicit Euler on dy/dt = -0.88 y with y(0)=25.5, step size h=1.95, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.1)=13.25 and f(11.1)=27.25.
3. The interval width is 4.
Final: {"answer": 81.0, "unit": "area_units"}

Answer: 81.0

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.5x+-11.6 from x=7.1 to x=11.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.1)=13.25 and f(11.1)=27.25.
The interval width is 4.


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": [-0.023, -0.844, -0.034], "unit": "temperature_units"}

Answer: -0.023

Answer: -0.844

Answer: -0.034

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=1.1, right=2.35; current interior values are [0.25, -1.65, -0.45]. Use r=0.26. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3286.0 / 100.
Final: {"answer": 32.86, "unit": "m"}

Answer: 32.86

Prompt: Convert 3286 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 3286.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=326 degrees and keep the unit as newtons.
Final: {"answer": [309.6455, -208.8585], "unit": "N"}

Answer: 309.6455

Answer: -208.8585

Prompt: A vector has magnitude 373.5 N at 326 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=326 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": [-6.05, 12.75], "unit": "dimensionless"}

Answer: -6.05

Answer: 12.75

Prompt: A line passes through points (-11.75, 83.8375) and (-5, 43). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 852203, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_006064(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_006064"}

Answer: python_code

Prompt: Write a Python function weighted_sum_006064(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_006064([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=0.06 and interior values [2.2, 3.0, -0.95], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16 kg and a = 7.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 125.6, "unit": "N"}

Answer: 125.6

Prompt: A cart has mass 16 kg and measured acceleration 7.85 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 = 16 kg and a = 7.85 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=62 degrees through the sine of 2 theta.
3. Substitute v=79.1 m/s and g=9.81 m/s^2.
Final: {"answer": 528.7595, "unit": "m"}

Answer: 528.7595

Prompt: A projectile is launched on level ground with no air resistance at speed 79.1 m/s and angle 62 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=62 degrees through the sine of 2 theta.
Substitute v=79.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.35 * 8.314 * 530 / 13.3.
Final: {"answer": 778.578, "unit": "kPa"}

Answer: 778.578

Prompt: An ideal gas sample has n=2.35 mol, T=530 K, and V=13.3 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 = 2.35 * 8.314 * 530 / 13.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 450 * 3.23 * 4.
Final: {"answer": 5814.0, "unit": "J"}

Answer: 5814.0

Prompt: A 450 g sample has specific heat 3.23 J/(g*K). How much heat is needed to raise its temperature by 4 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 450 * 3.23 * 4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=3.6 V and R=199.6 ohm.
Final: {"answer": 0.0649, "unit": "W"}

Answer: 0.0649

Prompt: A resistor has resistance 199.6 ohm and voltage 3.6 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=3.6 V and R=199.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=773 mg, t=271 h, and T_half=5.5 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 773 mg. Its half-life is 5.5 hours. How many mg remain after 271 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=773 mg, t=271 h, and T_half=5.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.92 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 229.0848, "unit": "g"}

Answer: 229.0848

Prompt: A sample contains 3.92 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.92 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.3)=-32.6 and f(-3.6)=-27.2.
3. The interval width is 2.7.
Final: {"answer": -80.73, "unit": "area_units"}

Answer: -80.73

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2x+-20 from x=-6.3 to x=-3.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.3)=-32.6 and f(-3.6)=-27.2.
The interval width is 2.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.18 and add it to the current value.
Final: {"answer": [0.492, 0.864, 1.459], "unit": "temperature_units"}

Answer: 0.492

Answer: 0.864

Answer: 1.459

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=0.45; current interior values are [-0.3, 0.9, 1.9]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 20980.0 / 1000.
Final: {"answer": 20.98, "unit": "kg"}

Answer: 20.98

Prompt: Convert 20980 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 20980.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=277 degrees and keep the unit as newtons.
Final: {"answer": [42.4105, -345.4061], "unit": "N"}

Answer: 42.4105

Answer: -345.4061

Prompt: A vector has magnitude 348 N at 277 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=277 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.95, 29.5], "unit": "dimensionless"}

Answer: 5.95

Answer: 29.5

Prompt: A line passes through points (14.75, 117.263) and (16.5, 127.675). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 187271, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_006082(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_006082"}

Answer: python_code

Prompt: Write a Python function running_total_006082(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 mobile invoice records in release 304058, 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 = 1.45 kg and a = 9.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 13.63, "unit": "N"}

Answer: 13.63

Prompt: A cart has mass 1.45 kg and measured acceleration 9.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.45 kg and a = 9.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 820 * 1.29 * 4.
Final: {"answer": 4231.2, "unit": "J"}

Answer: 4231.2

Prompt: A 820 g sample has specific heat 1.29 J/(g*K). How much heat is needed to raise its temperature by 4 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 820 * 1.29 * 4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=130.8 V and R=178.8 ohm.
Final: {"answer": 95.6859, "unit": "W"}

Answer: 95.6859

Prompt: A resistor has resistance 178.8 ohm and voltage 130.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=130.8 V and R=178.8 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.59 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 326.6796, "unit": "g"}

Answer: 326.6796

Prompt: A sample contains 5.59 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 = 5.59 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 700 mL to 0.7 L.
3. Compute M = 2.935 / 0.7.
Final: {"answer": 4.1929, "unit": "mol/L"}

Answer: 4.1929

Prompt: A solution contains 2.935 mol of solute in 700 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 700 mL to 0.7 L.
Compute M = 2.935 / 0.7.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.51 y with y(0)=76.5, step size h=2, 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) = -0.51 y, so each step multiplies y by 1 - h*0.51.
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(9.4)=41.28 and f(16.1)=82.82.
3. The interval width is 6.7.
Final: {"answer": 415.735, "unit": "area_units"}

Answer: 415.735

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.2x+-17 from x=9.4 to x=16.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.4)=41.28 and f(16.1)=82.82.
The interval width is 6.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [-0.109, -0.12, 1.018], "unit": "temperature_units"}

Answer: -0.109

Answer: -0.12

Answer: 1.018

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.15, right=1.5; current interior values are [-0.85, 1.4, -0.35]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 20866.0 / 1000.
Final: {"answer": 20.866, "unit": "kg"}

Answer: 20.866

Prompt: Convert 20866 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 20866.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=258 degrees and keep the unit as newtons.
Final: {"answer": [-26.8206, -126.181], "unit": "N"}

Answer: -26.8206

Answer: -126.181

Prompt: A vector has magnitude 129 N at 258 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=258 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.35, 1.0], "unit": "dimensionless"}

Answer: 1.35

Answer: 1.0

Prompt: A line passes through points (9.75, 14.1625) and (14, 19.9). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 student derivation case 3732, 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. 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 65.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 2.95 kg and a = 4.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 12.095, "unit": "N"}

Answer: 12.095

Prompt: A cart has mass 2.95 kg and measured acceleration 4.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.95 kg and a = 4.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=76 degrees through the sine of 2 theta.
3. Substitute v=65.3 m/s and g=9.81 m/s^2.
Final: {"answer": 204.0641, "unit": "m"}

Answer: 204.0641

Prompt: A projectile is launched on level ground with no air resistance at speed 65.3 m/s and angle 76 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=76 degrees through the sine of 2 theta.
Substitute v=65.3 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 = 3.89 * 8.314 * 360 / 62.1.
Final: {"answer": 187.4867, "unit": "kPa"}

Answer: 187.4867

Prompt: An ideal gas sample has n=3.89 mol, T=360 K, and V=62.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.89 * 8.314 * 360 / 62.1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=114.4 V and R=18.4 ohm.
Final: {"answer": 711.2696, "unit": "W"}

Answer: 711.2696

Prompt: A resistor has resistance 18.4 ohm and voltage 114.4 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=114.4 V and R=18.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=754.5 mg, t=322 h, and T_half=118 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 113.8163, "unit": "mg"}

Answer: 113.8163

Prompt: A radioactive sample starts with 754.5 mg. Its half-life is 118 hours. How many mg remain after 322 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=754.5 mg, t=322 h, and T_half=118 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.84 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 107.5296, "unit": "g"}

Answer: 107.5296

Prompt: A sample contains 1.84 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.84 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 2680 mL to 2.68 L.
3. Compute M = 4.64 / 2.68.
Final: {"answer": 1.7313, "unit": "mol/L"}

Answer: 1.7313

Prompt: A solution contains 4.64 mol of solute in 2680 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2680 mL to 2.68 L.
Compute M = 4.64 / 2.68.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 45.5398, "unit": "state_units"}

Answer: 45.5398

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=54, step size h=0.35, 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) = -0.08 y, so each step multiplies y by 1 - h*0.08.
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(7.7)=6.29 and f(9.6)=3.82.
3. The interval width is 1.9.
Final: {"answer": 9.6045, "unit": "area_units"}

Answer: 9.6045

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.3x+16.3 from x=7.7 to x=9.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.7)=6.29 and f(9.6)=3.82.
The interval width is 1.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.02 and add it to the current value.
Final: {"answer": [-0.325, 1.317, 1.401], "unit": "temperature_units"}

Answer: -0.325

Answer: 1.317

Answer: 1.401

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=1.6, right=-0.9; current interior values are [-0.4, 1.35, 1.45]. Use r=0.02. 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=0.02 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 46436.0 / 1000.
Final: {"answer": 46.436, "unit": "kg"}

Answer: 46.436

Prompt: Convert 46436 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 46436.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.95, 20.25], "unit": "dimensionless"}

Answer: -2.95

Answer: 20.25

Prompt: A line passes through points (17, -29.9) and (25.75, -55.7125). 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 lab notebook case 128848, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def center_values_006118(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_006118"}

Answer: python_code

Prompt: Write a Python function center_values_006118(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_006118([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 29.6^2 and multiply by 0.5 * 1.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 766.64, "unit": "J"}

Answer: 766.64

Prompt: A body of mass 1.75 kg moves at 29.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.6^2 and multiply by 0.5 * 1.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=78 degrees through the sine of 2 theta.
3. Substitute v=66.7 m/s and g=9.81 m/s^2.
Final: {"answer": 184.4573, "unit": "m"}

Answer: 184.4573

Prompt: A projectile is launched on level ground with no air resistance at speed 66.7 m/s and angle 78 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=78 degrees through the sine of 2 theta.
Substitute v=66.7 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 = 5.59 * 8.314 * 335 / 108.0.
Final: {"answer": 144.1594, "unit": "kPa"}

Answer: 144.1594

Prompt: An ideal gas sample has n=5.59 mol, T=335 K, and V=108.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.59 * 8.314 * 335 / 108.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 425 * 1.205 * 28.
Final: {"answer": 14339.5, "unit": "J"}

Answer: 14339.5

Prompt: A 425 g sample has specific heat 1.205 J/(g*K). How much heat is needed to raise its temperature by 28 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 425 * 1.205 * 28.


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=233 V and R=82.3 ohm.
Final: {"answer": 659.6476, "unit": "W"}

Answer: 659.6476

Prompt: A resistor has resistance 82.3 ohm and voltage 233 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=233 V and R=82.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=690 mg, t=207.5 h, and T_half=112 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 191.0457, "unit": "mg"}

Answer: 191.0457

Prompt: A radioactive sample starts with 690 mg. Its half-life is 112 hours. How many mg remain after 207.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=690 mg, t=207.5 h, and T_half=112 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 = 0.62 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 62.0539, "unit": "g"}

Answer: 62.0539

Prompt: A sample contains 0.62 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 = 0.62 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 150 mL to 0.15 L.
3. Compute M = 2.73 / 0.15.
Final: {"answer": 18.2, "unit": "mol/L"}

Answer: 18.2

Prompt: A solution contains 2.73 mol of solute in 150 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 150 mL to 0.15 L.
Compute M = 2.73 / 0.15.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 10.7547, "unit": "state_units"}

Answer: 10.7547

Prompt: Use explicit Euler on dy/dt = -0.78 y with y(0)=38.5, step size h=0.35, 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) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.2 and add it to the current value.
Final: {"answer": [0.49, 0.67, 0.33], "unit": "temperature_units"}

Answer: 0.49

Answer: 0.67

Answer: 0.33

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=2.15, right=1.35; current interior values are [-0.35, 1.35, -0.35]. Use r=0.2. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 84.5 + 273.15.
Final: {"answer": 357.65, "unit": "K"}

Answer: 357.65

Prompt: Convert 84.5 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 84.5 + 273.15.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.4, 5.75], "unit": "dimensionless"}

Answer: 4.4

Answer: 5.75

Prompt: A line passes through points (-7, -25.05) and (-6.75, -23.95). 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. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 907583, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_006136(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_006136"}

Answer: python_code

Prompt: Write a Python function weighted_sum_006136(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_006136([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a knapsack scoring problem with 4911 items and budget 5100, 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 = 41^2 and multiply by 0.5 * 2.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2185.3, "unit": "J"}

Answer: 2185.3

Prompt: A body of mass 2.6 kg moves at 41 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41^2 and multiply by 0.5 * 2.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=63 degrees through the sine of 2 theta.
3. Substitute v=39.5 m/s and g=9.81 m/s^2.
Final: {"answer": 128.6716, "unit": "m"}

Answer: 128.6716

Prompt: A projectile is launched on level ground with no air resistance at speed 39.5 m/s and angle 63 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=63 degrees through the sine of 2 theta.
Substitute v=39.5 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 = 1855 * 3.82 * 110.
Final: {"answer": 779471.0, "unit": "J"}

Answer: 779471.0

Prompt: A 1855 g sample has specific heat 3.82 J/(g*K). How much heat is needed to raise its temperature by 110 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1855 * 3.82 * 110.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=197.8 V and R=104 ohm.
Final: {"answer": 376.2004, "unit": "W"}

Answer: 376.2004

Prompt: A resistor has resistance 104 ohm and voltage 197.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=197.8 V and R=104 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=701 mg, t=208.5 h, and T_half=103.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 173.4983, "unit": "mg"}

Answer: 173.4983

Prompt: A radioactive sample starts with 701 mg. Its half-life is 103.5 hours. How many mg remain after 208.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=701 mg, t=208.5 h, and T_half=103.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 132.03, "unit": "g"}

Answer: 132.03

Prompt: A sample contains 3 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 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 4555 mL to 4.555 L.
3. Compute M = 4.41 / 4.555.
Final: {"answer": 0.9682, "unit": "mol/L"}

Answer: 0.9682

Prompt: A solution contains 4.41 mol of solute in 4555 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4555 mL to 4.555 L.
Compute M = 4.41 / 4.555.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.
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 = -0.87 y with y(0)=29, step size h=1.25, 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) = -0.87 y, so each step multiplies y by 1 - h*0.87.
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(-0.8)=11.58 and f(0.5)=17.3.
3. The interval width is 1.3.
Final: {"answer": 18.772, "unit": "area_units"}

Answer: 18.772

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+15.1 from x=-0.8 to x=0.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.8)=11.58 and f(0.5)=17.3.
The interval width is 1.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [2.131, 0.697, 0.468], "unit": "temperature_units"}

Answer: 2.131

Answer: 0.697

Answer: 0.468

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=2.15, right=-0.9; current interior values are [2.2, 2.1, -1.05]. Use r=0.46. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.46 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3075.0 / 100.
Final: {"answer": 30.75, "unit": "m"}

Answer: 30.75

Prompt: Convert 3075 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 3075.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=165 degrees and keep the unit as newtons.
Final: {"answer": [-14.9719, 4.0117], "unit": "N"}

Answer: -14.9719

Answer: 4.0117

Prompt: A vector has magnitude 15.5 N at 165 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=165 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.65, -8.75], "unit": "dimensionless"}

Answer: 7.65

Answer: -8.75

Prompt: A line passes through points (-13, -108.2) and (-5.25, -48.9125). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 930344, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def center_values_006154(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_006154"}

Answer: python_code

Prompt: Write a Python function center_values_006154(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_006154([])
    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)=48.5 and h=1.5, 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 = 11.25 kg and a = 6.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 74.25, "unit": "N"}

Answer: 74.25

Prompt: A cart has mass 11.25 kg and measured acceleration 6.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 11.25 kg and a = 6.6 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=85 degrees through the sine of 2 theta.
3. Substitute v=22.4 m/s and g=9.81 m/s^2.
Final: {"answer": 8.8817, "unit": "m"}

Answer: 8.8817

Prompt: A projectile is launched on level ground with no air resistance at speed 22.4 m/s and angle 85 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=85 degrees through the sine of 2 theta.
Substitute v=22.4 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 = 3.29 * 8.314 * 418 / 16.1.
Final: {"answer": 710.1602, "unit": "kPa"}

Answer: 710.1602

Prompt: An ideal gas sample has n=3.29 mol, T=418 K, and V=16.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.29 * 8.314 * 418 / 16.1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=1.1 V and R=86.2 ohm.
Final: {"answer": 0.014, "unit": "W"}

Answer: 0.014

Prompt: A resistor has resistance 86.2 ohm and voltage 1.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=1.1 V and R=86.2 ohm.


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 4 steps and round the final state.
Final: {"answer": 11.5329, "unit": "state_units"}

Answer: 11.5329

Prompt: Use explicit Euler on dy/dt = -0.06 y with y(0)=17.5, step size h=1.65, 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) = -0.06 y, so each step multiplies y by 1 - h*0.06.
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(5.8)=-18.3 and f(6.9)=-22.15.
3. The interval width is 1.1.
Final: {"answer": -22.2475, "unit": "area_units"}

Answer: -22.2475

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+2 from x=5.8 to x=6.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.8)=-18.3 and f(6.9)=-22.15.
The interval width is 1.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [0.91, 1.416, 1.762], "unit": "temperature_units"}

Answer: 0.91

Answer: 1.416

Answer: 1.762

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=0.65, right=1.4; current interior values are [0.35, 1.8, 2.05]. Use r=0.32. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.32 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 180.0 + 273.15.
Final: {"answer": 453.15, "unit": "K"}

Answer: 453.15

Prompt: Convert 180 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 180.0 + 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=112 degrees and keep the unit as newtons.
Final: {"answer": [-106.9502, 264.711], "unit": "N"}

Answer: -106.9502

Answer: 264.711

Prompt: A vector has magnitude 285.5 N at 112 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=112 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.85, 25.75], "unit": "dimensionless"}

Answer: -4.85

Answer: 25.75

Prompt: A line passes through points (4.25, 5.1375) and (17, -56.7). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In instrument manual case 792977, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def threshold_flags_006172(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_006172"}

Answer: python_code

Prompt: Write a Python function threshold_flags_006172(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_006172([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_006172([], 5) == []

assert threshold_flags_006172([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 20.3 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 = 23.55 kg and a = 12.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 286.1325, "unit": "N"}

Answer: 286.1325

Prompt: A cart has mass 23.55 kg and measured acceleration 12.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.55 kg and a = 12.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 25.2^2 and multiply by 0.5 * 12.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4080.132, "unit": "J"}

Answer: 4080.132

Prompt: A body of mass 12.85 kg moves at 25.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.2^2 and multiply by 0.5 * 12.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=55 degrees through the sine of 2 theta.
3. Substitute v=40.3 m/s and g=9.81 m/s^2.
Final: {"answer": 155.5704, "unit": "m"}

Answer: 155.5704

Prompt: A projectile is launched on level ground with no air resistance at speed 40.3 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=55 degrees through the sine of 2 theta.
Substitute v=40.3 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 = 3.59 * 8.314 * 587 / 44.8.
Final: {"answer": 391.0791, "unit": "kPa"}

Answer: 391.0791

Prompt: An ideal gas sample has n=3.59 mol, T=587 K, and V=44.8 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 = 3.59 * 8.314 * 587 / 44.8.


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=62.2 V and R=184.2 ohm.
Final: {"answer": 21.0035, "unit": "W"}

Answer: 21.0035

Prompt: A resistor has resistance 184.2 ohm and voltage 62.2 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=62.2 V and R=184.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=73 mg, t=360 h, and T_half=11 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 73 mg. Its half-life is 11 hours. How many mg remain after 360 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=73 mg, t=360 h, and T_half=11 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 = 0.07 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 3.0807, "unit": "g"}

Answer: 3.0807

Prompt: A sample contains 0.07 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.07 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 3755 mL to 3.755 L.
3. Compute M = 4.18 / 3.755.
Final: {"answer": 1.1132, "unit": "mol/L"}

Answer: 1.1132

Prompt: A solution contains 4.18 mol of solute in 3755 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3755 mL to 3.755 L.
Compute M = 4.18 / 3.755.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.1)=-7.68 and f(5.4)=-11.32.
3. The interval width is 1.3.
Final: {"answer": -12.35, "unit": "area_units"}

Answer: -12.35

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+3.8 from x=4.1 to x=5.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.1)=-7.68 and f(5.4)=-11.32.
The interval width is 1.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [0.06, -0.001, -0.54], "unit": "temperature_units"}

Answer: 0.06

Answer: -0.001

Answer: -0.54

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.6, right=-1; current interior values are [-0.15, -0.4, 0.3]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 123.0 + 273.15.
Final: {"answer": 396.15, "unit": "K"}

Answer: 396.15

Prompt: Convert 123 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 123.0 + 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=112 degrees and keep the unit as newtons.
Final: {"answer": [-88.5945, 219.279], "unit": "N"}

Answer: -88.5945

Answer: 219.279

Prompt: A vector has magnitude 236.5 N at 112 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=112 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": [-8.0, -24.0], "unit": "dimensionless"}

Answer: -8.0

Answer: -24.0

Prompt: A line passes through points (2.25, -42) and (2.75, -46). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 681747, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_006190(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_006190"}

Answer: python_code

Prompt: Write a Python function running_total_006190(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=0.3 and interior values [-0.45, 0.05, -1.8], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 19.7 kg and a = 0.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 14.775, "unit": "N"}

Answer: 14.775

Prompt: A cart has mass 19.7 kg and measured acceleration 0.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 19.7 kg and a = 0.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=18 degrees through the sine of 2 theta.
3. Substitute v=57.9 m/s and g=9.81 m/s^2.
Final: {"answer": 200.8662, "unit": "m"}

Answer: 200.8662

Prompt: A projectile is launched on level ground with no air resistance at speed 57.9 m/s and angle 18 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=18 degrees through the sine of 2 theta.
Substitute v=57.9 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 = 2.44 * 8.314 * 590 / 58.0.
Final: {"answer": 206.3592, "unit": "kPa"}

Answer: 206.3592

Prompt: An ideal gas sample has n=2.44 mol, T=590 K, and V=58.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.44 * 8.314 * 590 / 58.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 745 * 3.835 * 31.
Final: {"answer": 88569.325, "unit": "J"}

Answer: 88569.325

Prompt: A 745 g sample has specific heat 3.835 J/(g*K). How much heat is needed to raise its temperature by 31 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 745 * 3.835 * 31.


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=61.1 V and R=122.2 ohm.
Final: {"answer": 30.55, "unit": "W"}

Answer: 30.55

Prompt: A resistor has resistance 122.2 ohm and voltage 61.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=61.1 V and R=122.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=88.5 mg, t=200.5 h, and T_half=35.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.7651, "unit": "mg"}

Answer: 1.7651

Prompt: A radioactive sample starts with 88.5 mg. Its half-life is 35.5 hours. How many mg remain after 200.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=88.5 mg, t=200.5 h, and T_half=35.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4845 mL to 4.845 L.
3. Compute M = 4.31 / 4.845.
Final: {"answer": 0.8896, "unit": "mol/L"}

Answer: 0.8896

Prompt: A solution contains 4.31 mol of solute in 4845 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4845 mL to 4.845 L.
Compute M = 4.31 / 4.845.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0001, "unit": "state_units"}

Answer: 0.0001

Prompt: Use explicit Euler on dy/dt = -0.77 y with y(0)=9, step size h=0.9, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5)=-33.9 and f(-2.6)=-20.22.
3. The interval width is 2.4.
Final: {"answer": -64.944, "unit": "area_units"}

Answer: -64.944

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.7x+-5.4 from x=-5 to x=-2.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5)=-33.9 and f(-2.6)=-20.22.
The interval width is 2.4.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.36 and add it to the current value.
Final: {"answer": [-0.036, -0.654, -0.738], "unit": "temperature_units"}

Answer: -0.036

Answer: -0.654

Answer: -0.738

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-1.1; current interior values are [-0.9, -0.6, -0.45]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -52.5 + 273.15.
Final: {"answer": 220.65, "unit": "K"}

Answer: 220.65

Prompt: Convert -52.5 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 -52.5 + 273.15.


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 lab notebook case 962447, 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_006208(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_006208"}

Answer: python_code

Prompt: Write a Python function unit_vector_006208(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_006208(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: 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=0.25, 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 = 8.9 kg and a = 3.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 32.93, "unit": "N"}

Answer: 32.93

Prompt: A cart has mass 8.9 kg and measured acceleration 3.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 8.9 kg and a = 3.7 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=8 degrees through the sine of 2 theta.
3. Substitute v=81.5 m/s and g=9.81 m/s^2.
Final: {"answer": 186.6312, "unit": "m"}

Answer: 186.6312

Prompt: A projectile is launched on level ground with no air resistance at speed 81.5 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=8 degrees through the sine of 2 theta.
Substitute v=81.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.24 * 8.314 * 345 / 95.9.
Final: {"answer": 126.8167, "unit": "kPa"}

Answer: 126.8167

Prompt: An ideal gas sample has n=4.24 mol, T=345 K, and V=95.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.24 * 8.314 * 345 / 95.9.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=171.8 V and R=111.8 ohm.
Final: {"answer": 264.0004, "unit": "W"}

Answer: 264.0004

Prompt: A resistor has resistance 111.8 ohm and voltage 171.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=171.8 V and R=111.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=20.5 mg, t=134 h, and T_half=41.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 2.1865, "unit": "mg"}

Answer: 2.1865

Prompt: A radioactive sample starts with 20.5 mg. Its half-life is 41.5 hours. How many mg remain after 134 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=20.5 mg, t=134 h, and T_half=41.5 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 = 7.41 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 133.4912, "unit": "g"}

Answer: 133.4912

Prompt: A sample contains 7.41 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.41 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2700 mL to 2.7 L.
3. Compute M = 0.985 / 2.7.
Final: {"answer": 0.3648, "unit": "mol/L"}

Answer: 0.3648

Prompt: A solution contains 0.985 mol of solute in 2700 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2700 mL to 2.7 L.
Compute M = 0.985 / 2.7.


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": -0.2368, "unit": "state_units"}

Answer: -0.2368

Prompt: Use explicit Euler on dy/dt = -0.81 y with y(0)=45.5, step size h=2, 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. 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=0.28 and add it to the current value.
Final: {"answer": [0.682, 0.912, 1.328], "unit": "temperature_units"}

Answer: 0.682

Answer: 0.912

Answer: 1.328

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=1.6, right=1; current interior values are [-0.2, 1.15, 1.65]. Use r=0.28. 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=0.28 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 4853.5 / 100.
Final: {"answer": 48.535, "unit": "m"}

Answer: 48.535

Prompt: Convert 4853.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4853.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=321 degrees and keep the unit as newtons.
Final: {"answer": [235.8638, -190.9987], "unit": "N"}

Answer: 235.8638

Answer: -190.9987

Prompt: A vector has magnitude 303.5 N at 321 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=321 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": [6.45, -25.0], "unit": "dimensionless"}

Answer: 6.45

Answer: -25.0

Prompt: A line passes through points (19.25, 99.1625) and (25.25, 137.863). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 643001, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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_006226(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_006226"}

Answer: python_code

Prompt: Write a Python function finite_differences_006226(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_006226([5]) == []

assert finite_differences_006226([]) == []


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.1 kg and a = 0.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 13.68, "unit": "N"}

Answer: 13.68

Prompt: A cart has mass 17.1 kg and measured acceleration 0.8 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 = 17.1 kg and a = 0.8 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 = 27.65^2 and multiply by 0.5 * 19.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7454.0944, "unit": "J"}

Answer: 7454.0944

Prompt: A body of mass 19.5 kg moves at 27.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 27.65^2 and multiply by 0.5 * 19.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=62 degrees through the sine of 2 theta.
3. Substitute v=16.8 m/s and g=9.81 m/s^2.
Final: {"answer": 23.8519, "unit": "m"}

Answer: 23.8519

Prompt: A projectile is launched on level ground with no air resistance at speed 16.8 m/s and angle 62 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=62 degrees through the sine of 2 theta.
Substitute v=16.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 360 * 0.985 * 95.
Final: {"answer": 33687.0, "unit": "J"}

Answer: 33687.0

Prompt: A 360 g sample has specific heat 0.985 J/(g*K). How much heat is needed to raise its temperature by 95 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 360 * 0.985 * 95.


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=75 V and R=103.6 ohm.
Final: {"answer": 54.2954, "unit": "W"}

Answer: 54.2954

Prompt: A resistor has resistance 103.6 ohm and voltage 75 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=75 V and R=103.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=297 mg, t=62 h, and T_half=12 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 8.2687, "unit": "mg"}

Answer: 8.2687

Prompt: A radioactive sample starts with 297 mg. Its half-life is 12 hours. How many mg remain after 62 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=297 mg, t=62 h, and T_half=12 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.46 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 240.2946, "unit": "g"}

Answer: 240.2946

Prompt: A sample contains 5.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.46 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 970 mL to 0.97 L.
3. Compute M = 3.38 / 0.97.
Final: {"answer": 3.4845, "unit": "mol/L"}

Answer: 3.4845

Prompt: A solution contains 3.38 mol of solute in 970 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 970 mL to 0.97 L.
Compute M = 3.38 / 0.97.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.1712, "unit": "state_units"}

Answer: 0.1712

Prompt: Use explicit Euler on dy/dt = -0.12 y with y(0)=1, step size h=1.65, 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) = -0.12 y, so each step multiplies y by 1 - h*0.12.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.8)=-34.56 and f(0.9)=0.28.
3. The interval width is 6.7.
Final: {"answer": -114.838, "unit": "area_units"}

Answer: -114.838

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.2x+-4.4 from x=-5.8 to x=0.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.8)=-34.56 and f(0.9)=0.28.
The interval width is 6.7.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 23497.0 / 1000.
Final: {"answer": 23.497, "unit": "kg"}

Answer: 23.497

Prompt: Convert 23497 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 23497.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.9, -8.5], "unit": "dimensionless"}

Answer: -5.9

Answer: -8.5

Prompt: A line passes through points (-19.75, 108.025) and (-5.5, 23.95). 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. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In sensor calibration case 309894, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_006244(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_006244"}

Answer: python_code

Prompt: Write a Python function finite_differences_006244(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_006244([5]) == []

assert finite_differences_006244([]) == []


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.65 kg and a = 0.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 0.9075, "unit": "N"}

Answer: 0.9075

Prompt: A cart has mass 1.65 kg and measured acceleration 0.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.65 kg and a = 0.55 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=13 degrees through the sine of 2 theta.
3. Substitute v=75 m/s and g=9.81 m/s^2.
Final: {"answer": 251.3596, "unit": "m"}

Answer: 251.3596

Prompt: A projectile is launched on level ground with no air resistance at speed 75 m/s and angle 13 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=13 degrees through the sine of 2 theta.
Substitute v=75 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 = 1075 * 3.86 * 16.
Final: {"answer": 66392.0, "unit": "J"}

Answer: 66392.0

Prompt: A 1075 g sample has specific heat 3.86 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1075 * 3.86 * 16.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=165.3 V and R=41.7 ohm.
Final: {"answer": 655.254, "unit": "W"}

Answer: 655.254

Prompt: A resistor has resistance 41.7 ohm and voltage 165.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=165.3 V and R=41.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=577.5 mg, t=15 h, and T_half=81.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 508.3323, "unit": "mg"}

Answer: 508.3323

Prompt: A radioactive sample starts with 577.5 mg. Its half-life is 81.5 hours. How many mg remain after 15 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=577.5 mg, t=15 h, and T_half=81.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1885 mL to 1.885 L.
3. Compute M = 2.01 / 1.885.
Final: {"answer": 1.0663, "unit": "mol/L"}

Answer: 1.0663

Prompt: A solution contains 2.01 mol of solute in 1885 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1885 mL to 1.885 L.
Compute M = 2.01 / 1.885.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 6.4823, "unit": "state_units"}

Answer: 6.4823

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=9.5, step size h=0.25, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
Apply that update for 10 steps and round the final state.