Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.5 kg and a = 6.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 35.475, "unit": "N"}

Answer: 35.475

Prompt: A cart has mass 5.5 kg and measured acceleration 6.45 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 = 5.5 kg and a = 6.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.75^2 and multiply by 0.5 * 18.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9299.3766, "unit": "J"}

Answer: 9299.3766

Prompt: A body of mass 18.45 kg moves at 31.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.75^2 and multiply by 0.5 * 18.45.
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=73 degrees through the sine of 2 theta.
3. Substitute v=66 m/s and g=9.81 m/s^2.
Final: {"answer": 248.3022, "unit": "m"}

Answer: 248.3022

Prompt: A projectile is launched on level ground with no air resistance at speed 66 m/s and angle 73 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=73 degrees through the sine of 2 theta.
Substitute v=66 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 * 410 / 80.0.
Final: {"answer": 109.0797, "unit": "kPa"}

Answer: 109.0797

Prompt: An ideal gas sample has n=2.56 mol, T=410 K, and V=80.0 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 = 2.56 * 8.314 * 410 / 80.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1855 * 3.61 * 52.
Final: {"answer": 348220.6, "unit": "J"}

Answer: 348220.6

Prompt: A 1855 g sample has specific heat 3.61 J/(g*K). How much heat is needed to raise its temperature by 52 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1855 * 3.61 * 52.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=308.5 mg, t=31.5 h, and T_half=17 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 85.4013, "unit": "mg"}

Answer: 85.4013

Prompt: A radioactive sample starts with 308.5 mg. Its half-life is 17 hours. How many mg remain after 31.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=308.5 mg, t=31.5 h, and T_half=17 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 = 7.51 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1352.9716, "unit": "g"}

Answer: 1352.9716

Prompt: A sample contains 7.51 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.51 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1975 mL to 1.975 L.
3. Compute M = 1.705 / 1.975.
Final: {"answer": 0.8633, "unit": "mol/L"}

Answer: 0.8633

Prompt: A solution contains 1.705 mol of solute in 1975 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1975 mL to 1.975 L.
Compute M = 1.705 / 1.975.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.3 and add it to the current value.
Final: {"answer": [0.0, 0.965, 1.62], "unit": "temperature_units"}

Answer: 0.0

Answer: 0.965

Answer: 1.62

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=-0.85, right=1.95; current interior values are [0.6, 0.05, 2.55]. Use r=0.3. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 183.0 + 273.15.
Final: {"answer": 456.15, "unit": "K"}

Answer: 456.15

Prompt: Convert 183 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 183.0 + 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=255 degrees and keep the unit as newtons.
Final: {"answer": [-84.2456, -314.4089], "unit": "N"}

Answer: -84.2456

Answer: -314.4089

Prompt: A vector has magnitude 325.5 N at 255 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=255 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.05, -22.5], "unit": "dimensionless"}

Answer: -0.05

Answer: -22.5

Prompt: A line passes through points (-3.25, -22.3375) and (3, -22.65). 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 sensor calibration case 670493, 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_001150(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_001150"}

Answer: python_code

Prompt: Write a Python function threshold_flags_001150(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_001150([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_001150([], 5) == []

assert threshold_flags_001150([-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 20.4 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 = 21.6 kg and a = 2.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 55.08, "unit": "N"}

Answer: 55.08

Prompt: A cart has mass 21.6 kg and measured acceleration 2.55 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 = 21.6 kg and a = 2.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.9^2 and multiply by 0.5 * 26.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 47.8325, "unit": "J"}

Answer: 47.8325

Prompt: A body of mass 26.5 kg moves at 1.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.9^2 and multiply by 0.5 * 26.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.54 * 8.314 * 618 / 52.1.
Final: {"answer": 447.7304, "unit": "kPa"}

Answer: 447.7304

Prompt: An ideal gas sample has n=4.54 mol, T=618 K, and V=52.1 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 = 4.54 * 8.314 * 618 / 52.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1345 * 4.635 * 10.
Final: {"answer": 62340.75, "unit": "J"}

Answer: 62340.75

Prompt: A 1345 g sample has specific heat 4.635 J/(g*K). How much heat is needed to raise its temperature by 10 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1345 * 4.635 * 10.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=464 mg, t=226.5 h, and T_half=14.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0092, "unit": "mg"}

Answer: 0.0092

Prompt: A radioactive sample starts with 464 mg. Its half-life is 14.5 hours. How many mg remain after 226.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=464 mg, t=226.5 h, and T_half=14.5 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 4405 mL to 4.405 L.
3. Compute M = 2.69 / 4.405.
Final: {"answer": 0.6107, "unit": "mol/L"}

Answer: 0.6107

Prompt: A solution contains 2.69 mol of solute in 4405 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4405 mL to 4.405 L.
Compute M = 2.69 / 4.405.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.5)=0.5 and f(-0.7)=-5.3.
3. The interval width is 5.8.
Final: {"answer": -13.92, "unit": "area_units"}

Answer: -13.92

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1x+-6 from x=-6.5 to x=-0.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.5)=0.5 and f(-0.7)=-5.3.
The interval width is 5.8.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [1.11, 1.114, 0.274], "unit": "temperature_units"}

Answer: 1.11

Answer: 1.114

Answer: 0.274

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=0.75, right=-0.95; current interior values are [1.35, 1.45, 0.85]. Use r=0.48. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1923.5 / 100.
Final: {"answer": 19.235, "unit": "m"}

Answer: 19.235

Prompt: Convert 1923.5 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 1923.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=315 degrees and keep the unit as newtons.
Final: {"answer": [59.397, -59.397], "unit": "N"}

Answer: 59.397

Answer: -59.397

Prompt: A vector has magnitude 84 N at 315 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=315 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.75, 2.0], "unit": "dimensionless"}

Answer: -0.75

Answer: 2.0

Prompt: A line passes through points (5, -1.75) and (18.75, -12.0625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In instrument manual case 887782, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def threshold_flags_001168(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_001168"}

Answer: python_code

Prompt: Write a Python function threshold_flags_001168(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_001168([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_001168([], 5) == []

assert threshold_flags_001168([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 0.6 kg and a = 5.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 3.39, "unit": "N"}

Answer: 3.39

Prompt: A cart has mass 0.6 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 0.6 kg and a = 5.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 42.25^2 and multiply by 0.5 * 5.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4730.4156, "unit": "J"}

Answer: 4730.4156

Prompt: A body of mass 5.3 kg moves at 42.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.25^2 and multiply by 0.5 * 5.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=25 degrees through the sine of 2 theta.
3. Substitute v=79.9 m/s and g=9.81 m/s^2.
Final: {"answer": 498.5153, "unit": "m"}

Answer: 498.5153

Prompt: A projectile is launched on level ground with no air resistance at speed 79.9 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=25 degrees through the sine of 2 theta.
Substitute v=79.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 700 * 4.525 * 104.
Final: {"answer": 329420.0, "unit": "J"}

Answer: 329420.0

Prompt: A 700 g sample has specific heat 4.525 J/(g*K). How much heat is needed to raise its temperature by 104 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 700 * 4.525 * 104.


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=150.9 V and R=105.8 ohm.
Final: {"answer": 215.225, "unit": "W"}

Answer: 215.225

Prompt: A resistor has resistance 105.8 ohm and voltage 150.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=150.9 V and R=105.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=817.5 mg, t=242.5 h, and T_half=52 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 32.2586, "unit": "mg"}

Answer: 32.2586

Prompt: A radioactive sample starts with 817.5 mg. Its half-life is 52 hours. How many mg remain after 242.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=817.5 mg, t=242.5 h, and T_half=52 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 3375 mL to 3.375 L.
3. Compute M = 2.69 / 3.375.
Final: {"answer": 0.797, "unit": "mol/L"}

Answer: 0.797

Prompt: A solution contains 2.69 mol of solute in 3375 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3375 mL to 3.375 L.
Compute M = 2.69 / 3.375.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.1364, "unit": "state_units"}

Answer: 0.1364

Prompt: Use explicit Euler on dy/dt = -0.5 y with y(0)=25, step size h=1.05, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.
Apply that update for 7 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=0.14 and add it to the current value.
Final: {"answer": [-0.832, -0.044, -0.853], "unit": "temperature_units"}

Answer: -0.832

Answer: -0.044

Answer: -0.853

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=2.2, right=2.05; current interior values are [-1.7, 0.6, -1.7]. Use r=0.14. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 40.5 + 273.15.
Final: {"answer": 313.65, "unit": "K"}

Answer: 313.65

Prompt: Convert 40.5 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 40.5 + 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": [-3.8, 3.25], "unit": "dimensionless"}

Answer: -3.8

Answer: 3.25

Prompt: A line passes through points (1.75, -3.4) and (6.75, -22.4). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def clamp_001186(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_001186"}

Answer: python_code

Prompt: Write a Python function clamp_001186(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_001186(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.1 kg and a = 11.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 119.685, "unit": "N"}

Answer: 119.685

Prompt: A cart has mass 10.1 kg and measured acceleration 11.85 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 = 10.1 kg and a = 11.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 34.75^2 and multiply by 0.5 * 2.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1690.5875, "unit": "J"}

Answer: 1690.5875

Prompt: A body of mass 2.8 kg moves at 34.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.75^2 and multiply by 0.5 * 2.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=39 degrees through the sine of 2 theta.
3. Substitute v=80.4 m/s and g=9.81 m/s^2.
Final: {"answer": 644.5365, "unit": "m"}

Answer: 644.5365

Prompt: A projectile is launched on level ground with no air resistance at speed 80.4 m/s and angle 39 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=39 degrees through the sine of 2 theta.
Substitute v=80.4 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 = 3.64 * 8.314 * 374 / 115.1.
Final: {"answer": 98.3349, "unit": "kPa"}

Answer: 98.3349

Prompt: An ideal gas sample has n=3.64 mol, T=374 K, and V=115.1 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 = 3.64 * 8.314 * 374 / 115.1.


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=34.2 V and R=6.2 ohm.
Final: {"answer": 188.6516, "unit": "W"}

Answer: 188.6516

Prompt: A resistor has resistance 6.2 ohm and voltage 34.2 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=34.2 V and R=6.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=596.5 mg, t=310 h, and T_half=13 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 596.5 mg. Its half-life is 13 hours. How many mg remain after 310 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=596.5 mg, t=310 h, and T_half=13 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.96 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 406.7424, "unit": "g"}

Answer: 406.7424

Prompt: A sample contains 6.96 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.96 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.015, "unit": "state_units"}

Answer: 0.015

Prompt: Use explicit Euler on dy/dt = -0.3 y with y(0)=78.5, step size h=1.7, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.7)=-5.46 and f(-1.4)=7.68.
3. The interval width is 7.3.
Final: {"answer": 8.103, "unit": "area_units"}

Answer: 8.103

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.8x+10.2 from x=-8.7 to x=-1.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.7)=-5.46 and f(-1.4)=7.68.
The interval width is 7.3.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 240.0 + 273.15.
Final: {"answer": 513.15, "unit": "K"}

Answer: 513.15

Prompt: Convert 240 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 240.0 + 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=167 degrees and keep the unit as newtons.
Final: {"answer": [-145.6683, 33.6302], "unit": "N"}

Answer: -145.6683

Answer: 33.6302

Prompt: A vector has magnitude 149.5 N at 167 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=167 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": [6.9, 23.25], "unit": "dimensionless"}

Answer: 6.9

Answer: 23.25

Prompt: A line passes through points (-3.25, 0.825) and (7, 71.55). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 819147, 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
import math

def unit_vector_001204(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_001204"}

Answer: python_code

Prompt: Write a Python function unit_vector_001204(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_001204(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid mobile ledger records in release 252611, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.9^2 and multiply by 0.5 * 26.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9533.5617, "unit": "J"}

Answer: 9533.5617

Prompt: A body of mass 26.35 kg moves at 26.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.9^2 and multiply by 0.5 * 26.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=48 degrees through the sine of 2 theta.
3. Substitute v=29.7 m/s and g=9.81 m/s^2.
Final: {"answer": 89.4249, "unit": "m"}

Answer: 89.4249

Prompt: A projectile is launched on level ground with no air resistance at speed 29.7 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=48 degrees through the sine of 2 theta.
Substitute v=29.7 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 = 1.96 * 8.314 * 584 / 49.2.
Final: {"answer": 193.4255, "unit": "kPa"}

Answer: 193.4255

Prompt: An ideal gas sample has n=1.96 mol, T=584 K, and V=49.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.96 * 8.314 * 584 / 49.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 130 * 3.365 * 91.
Final: {"answer": 39807.95, "unit": "J"}

Answer: 39807.95

Prompt: A 130 g sample has specific heat 3.365 J/(g*K). How much heat is needed to raise its temperature by 91 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 130 * 3.365 * 91.


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=216 V and R=32.7 ohm.
Final: {"answer": 1426.789, "unit": "W"}

Answer: 1426.789

Prompt: A resistor has resistance 32.7 ohm and voltage 216 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=216 V and R=32.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=456 mg, t=265.5 h, and T_half=49.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 11.0751, "unit": "mg"}

Answer: 11.0751

Prompt: A radioactive sample starts with 456 mg. Its half-life is 49.5 hours. How many mg remain after 265.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=456 mg, t=265.5 h, and T_half=49.5 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 3330 mL to 3.33 L.
3. Compute M = 3.84 / 3.33.
Final: {"answer": 1.1532, "unit": "mol/L"}

Answer: 1.1532

Prompt: A solution contains 3.84 mol of solute in 3330 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3330 mL to 3.33 L.
Compute M = 3.84 / 3.33.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 4.223, "unit": "state_units"}

Answer: 4.223

Prompt: Use explicit Euler on dy/dt = -0.57 y with y(0)=25, step size h=0.45, 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) = -0.57 y, so each step multiplies y by 1 - h*0.57.
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(7.5)=18.7 and f(10.8)=27.94.
3. The interval width is 3.3.
Final: {"answer": 76.956, "unit": "area_units"}

Answer: 76.956

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.8x+-2.3 from x=7.5 to x=10.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.5)=18.7 and f(10.8)=27.94.
The interval width is 3.3.


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": [-0.758, 1.172, -0.19], "unit": "temperature_units"}

Answer: -0.758

Answer: 1.172

Answer: -0.19

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.35, right=-0.95; current interior values are [0.25, -0.55, 2.75]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4071.5 / 100.
Final: {"answer": 40.715, "unit": "m"}

Answer: 40.715

Prompt: Convert 4071.5 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 4071.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=17 degrees and keep the unit as newtons.
Final: {"answer": [330.4033, 101.0144], "unit": "N"}

Answer: 330.4033

Answer: 101.0144

Prompt: A vector has magnitude 345.5 N at 17 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=17 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": [-6.1, 16.75], "unit": "dimensionless"}

Answer: -6.1

Answer: 16.75

Prompt: A line passes through points (3.5, -4.6) and (8.25, -33.575). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In sensor calibration case 544001, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_001222(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_001222"}

Answer: python_code

Prompt: Write a Python function running_total_001222(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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 15.2^2 and multiply by 0.5 * 14.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1634.608, "unit": "J"}

Answer: 1634.608

Prompt: A body of mass 14.15 kg moves at 15.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.2^2 and multiply by 0.5 * 14.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=77 degrees through the sine of 2 theta.
3. Substitute v=45.7 m/s and g=9.81 m/s^2.
Final: {"answer": 93.3266, "unit": "m"}

Answer: 93.3266

Prompt: A projectile is launched on level ground with no air resistance at speed 45.7 m/s and angle 77 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=77 degrees through the sine of 2 theta.
Substitute v=45.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.27 * 8.314 * 366 / 87.8.
Final: {"answer": 78.6724, "unit": "kPa"}

Answer: 78.6724

Prompt: An ideal gas sample has n=2.27 mol, T=366 K, and V=87.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.27 * 8.314 * 366 / 87.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 865 * 2 * 21.
Final: {"answer": 36330.0, "unit": "J"}

Answer: 36330.0

Prompt: A 865 g sample has specific heat 2 J/(g*K). How much heat is needed to raise its temperature by 21 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 865 * 2 * 21.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=974 mg, t=348.5 h, and T_half=117.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 124.657, "unit": "mg"}

Answer: 124.657

Prompt: A radioactive sample starts with 974 mg. Its half-life is 117.5 hours. How many mg remain after 348.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=974 mg, t=348.5 h, and T_half=117.5 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 3245 mL to 3.245 L.
3. Compute M = 3.56 / 3.245.
Final: {"answer": 1.0971, "unit": "mol/L"}

Answer: 1.0971

Prompt: A solution contains 3.56 mol of solute in 3245 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3245 mL to 3.245 L.
Compute M = 3.56 / 3.245.


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 6 steps and round the final state.
Final: {"answer": 5.7168, "unit": "state_units"}

Answer: 5.7168

Prompt: Use explicit Euler on dy/dt = -0.87 y with y(0)=18, step size h=0.2, 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) = -0.87 y, so each step multiplies y by 1 - h*0.87.
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(3.9)=19.11 and f(7.7)=33.93.
3. The interval width is 3.8.
Final: {"answer": 100.776, "unit": "area_units"}

Answer: 100.776

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.9x+3.9 from x=3.9 to x=7.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.9)=19.11 and f(7.7)=33.93.
The interval width is 3.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [1.086, 1.572, 1.746], "unit": "temperature_units"}

Answer: 1.086

Answer: 1.572

Answer: 1.746

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=2.05; current interior values are [0.35, 1.25, 2.85]. 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 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 9826.0 / 1000.
Final: {"answer": 9.826, "unit": "kg"}

Answer: 9.826

Prompt: Convert 9826 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 9826.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=275 degrees and keep the unit as newtons.
Final: {"answer": [4.1835, -47.8173], "unit": "N"}

Answer: 4.1835

Answer: -47.8173

Prompt: A vector has magnitude 48 N at 275 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=275 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [0.55, -17.25], "unit": "dimensionless"}

Answer: 0.55

Answer: -17.25

Prompt: A line passes through points (-11.25, -23.4375) and (0, -17.25). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 172907, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. 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=0.14 and interior values [0.75, -0.6, 2.05], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.3^2 and multiply by 0.5 * 17.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 8351.8573, "unit": "J"}

Answer: 8351.8573

Prompt: A body of mass 17.05 kg moves at 31.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.3^2 and multiply by 0.5 * 17.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=50 degrees through the sine of 2 theta.
3. Substitute v=74.5 m/s and g=9.81 m/s^2.
Final: {"answer": 557.1793, "unit": "m"}

Answer: 557.1793

Prompt: A projectile is launched on level ground with no air resistance at speed 74.5 m/s and angle 50 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=50 degrees through the sine of 2 theta.
Substitute v=74.5 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 = 3.12 * 8.314 * 415 / 22.4.
Final: {"answer": 480.5789, "unit": "kPa"}

Answer: 480.5789

Prompt: An ideal gas sample has n=3.12 mol, T=415 K, and V=22.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.12 * 8.314 * 415 / 22.4.


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=35.2 V and R=146.1 ohm.
Final: {"answer": 8.4808, "unit": "W"}

Answer: 8.4808

Prompt: A resistor has resistance 146.1 ohm and voltage 35.2 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=35.2 V and R=146.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=930 mg, t=63.5 h, and T_half=38 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 292.0424, "unit": "mg"}

Answer: 292.0424

Prompt: A radioactive sample starts with 930 mg. Its half-life is 38 hours. How many mg remain after 63.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=930 mg, t=63.5 h, and T_half=38 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 = 2.14 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 214.1862, "unit": "g"}

Answer: 214.1862

Prompt: A sample contains 2.14 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 = 2.14 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 540 mL to 0.54 L.
3. Compute M = 0.16 / 0.54.
Final: {"answer": 0.2963, "unit": "mol/L"}

Answer: 0.2963

Prompt: A solution contains 0.16 mol of solute in 540 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 540 mL to 0.54 L.
Compute M = 0.16 / 0.54.


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 9 steps and round the final state.
Final: {"answer": 12.0934, "unit": "state_units"}

Answer: 12.0934

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=13, step size h=0.1, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.8)=5.02 and f(12.9)=12.81.
3. The interval width is 4.1.
Final: {"answer": 36.5515, "unit": "area_units"}

Answer: 36.5515

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-11.7 from x=8.8 to x=12.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.8)=5.02 and f(12.9)=12.81.
The interval width is 4.1.


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=0.18 and add it to the current value.
Final: {"answer": [0.783, -0.165, -0.237], "unit": "temperature_units"}

Answer: 0.783

Answer: -0.165

Answer: -0.237

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=1.65; current interior values are [0.9, -0.3, -0.75]. 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 18459.0 / 1000.
Final: {"answer": 18.459, "unit": "kg"}

Answer: 18.459

Prompt: Convert 18459 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 18459.0 / 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": [8.35, -18.25], "unit": "dimensionless"}

Answer: 8.35

Answer: -18.25

Prompt: A line passes through points (-1.75, -32.8625) and (7.5, 44.375). 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 699814, 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_001258(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_001258"}

Answer: python_code

Prompt: Write a Python function running_total_001258(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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=32 degrees through the sine of 2 theta.
3. Substitute v=75 m/s and g=9.81 m/s^2.
Final: {"answer": 515.3636, "unit": "m"}

Answer: 515.3636

Prompt: A projectile is launched on level ground with no air resistance at speed 75 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=32 degrees through the sine of 2 theta.
Substitute v=75 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 = 3.81 * 8.314 * 494 / 73.9.
Final: {"answer": 211.7471, "unit": "kPa"}

Answer: 211.7471

Prompt: An ideal gas sample has n=3.81 mol, T=494 K, and V=73.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.81 * 8.314 * 494 / 73.9.


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=174.9 V and R=168.6 ohm.
Final: {"answer": 181.4354, "unit": "W"}

Answer: 181.4354

Prompt: A resistor has resistance 168.6 ohm and voltage 174.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=174.9 V and R=168.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=250.5 mg, t=259.5 h, and T_half=35 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.4685, "unit": "mg"}

Answer: 1.4685

Prompt: A radioactive sample starts with 250.5 mg. Its half-life is 35 hours. How many mg remain after 259.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=250.5 mg, t=259.5 h, and T_half=35 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 = 1.27 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 22.879, "unit": "g"}

Answer: 22.879

Prompt: A sample contains 1.27 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.27 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 30 mL to 0.03 L.
3. Compute M = 3.93 / 0.03.
Final: {"answer": 131.0, "unit": "mol/L"}

Answer: 131.0

Prompt: A solution contains 3.93 mol of solute in 30 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 30 mL to 0.03 L.
Compute M = 3.93 / 0.03.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 2.6804, "unit": "state_units"}

Answer: 2.6804

Prompt: Use explicit Euler on dy/dt = -0.37 y with y(0)=15.5, step size h=0.8, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.3)=6.72 and f(-3.3)=5.52.
3. The interval width is 3.
Final: {"answer": 18.36, "unit": "area_units"}

Answer: 18.36

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+4.2 from x=-6.3 to x=-3.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.3)=6.72 and f(-3.3)=5.52.
The interval width is 3.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 18807.0 / 1000.
Final: {"answer": 18.807, "unit": "kg"}

Answer: 18.807

Prompt: Convert 18807 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 18807.0 / 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": [-4.6, 14.75], "unit": "dimensionless"}

Answer: -4.6

Answer: 14.75

Prompt: A line passes through points (-11.75, 68.8) and (-11.5, 67.65). 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 instrument manual case 935652, 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 safe_mean_001276(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_001276"}

Answer: python_code

Prompt: Write a Python function safe_mean_001276(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_001276([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing crop records in release 571753, 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 = 22.55 kg and a = 3.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 83.435, "unit": "N"}

Answer: 83.435

Prompt: A cart has mass 22.55 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 = 22.55 kg and a = 3.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.2^2 and multiply by 0.5 * 6.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1142.784, "unit": "J"}

Answer: 1142.784

Prompt: A body of mass 6.2 kg moves at 19.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.2^2 and multiply by 0.5 * 6.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=19 degrees through the sine of 2 theta.
3. Substitute v=11.7 m/s and g=9.81 m/s^2.
Final: {"answer": 8.591, "unit": "m"}

Answer: 8.591

Prompt: A projectile is launched on level ground with no air resistance at speed 11.7 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=19 degrees through the sine of 2 theta.
Substitute v=11.7 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 = 1390 * 4.095 * 112.
Final: {"answer": 637509.6, "unit": "J"}

Answer: 637509.6

Prompt: A 1390 g sample has specific heat 4.095 J/(g*K). How much heat is needed to raise its temperature by 112 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1390 * 4.095 * 112.


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=146.5 V and R=127.3 ohm.
Final: {"answer": 168.5958, "unit": "W"}

Answer: 168.5958

Prompt: A resistor has resistance 127.3 ohm and voltage 146.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=146.5 V and R=127.3 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3800 mL to 3.8 L.
3. Compute M = 1.345 / 3.8.
Final: {"answer": 0.3539, "unit": "mol/L"}

Answer: 0.3539

Prompt: A solution contains 1.345 mol of solute in 3800 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3800 mL to 3.8 L.
Compute M = 1.345 / 3.8.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 11.8011, "unit": "state_units"}

Answer: 11.8011

Prompt: Use explicit Euler on dy/dt = -0.43 y with y(0)=74.5, step size h=1.4, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5)=10.6 and f(11.4)=1.
3. The interval width is 6.4.
Final: {"answer": 37.12, "unit": "area_units"}

Answer: 37.12

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+18.1 from x=5 to x=11.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5)=10.6 and f(11.4)=1.
The interval width is 6.4.


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=0.38 and add it to the current value.
Final: {"answer": [1.056, 1.805, 1.221], "unit": "temperature_units"}

Answer: 1.056

Answer: 1.805

Answer: 1.221

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.5, right=-0.55; current interior values are [0.6, 1.9, 2.95]. 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 30176.0 / 1000.
Final: {"answer": 30.176, "unit": "kg"}

Answer: 30.176

Prompt: Convert 30176 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 30176.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=12 degrees and keep the unit as newtons.
Final: {"answer": [152.102, 32.3303], "unit": "N"}

Answer: 152.102

Answer: 32.3303

Prompt: A vector has magnitude 155.5 N at 12 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=12 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": [3.35, 11.0], "unit": "dimensionless"}

Answer: 3.35

Answer: 11.0

Prompt: A line passes through points (-3, 0.95) and (6.75, 33.6125). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In sensor calibration case 538379, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_001294(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_001294"}

Answer: python_code

Prompt: Write a Python function running_total_001294(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=57 and h=0.55, 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=9 degrees through the sine of 2 theta.
3. Substitute v=25.5 m/s and g=9.81 m/s^2.
Final: {"answer": 20.483, "unit": "m"}

Answer: 20.483

Prompt: A projectile is launched on level ground with no air resistance at speed 25.5 m/s and angle 9 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=9 degrees through the sine of 2 theta.
Substitute v=25.5 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 = 5.51 * 8.314 * 386 / 56.8.
Final: {"answer": 311.3154, "unit": "kPa"}

Answer: 311.3154

Prompt: An ideal gas sample has n=5.51 mol, T=386 K, and V=56.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.51 * 8.314 * 386 / 56.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1635 * 1.03 * 78.
Final: {"answer": 131355.9, "unit": "J"}

Answer: 131355.9

Prompt: A 1635 g sample has specific heat 1.03 J/(g*K). How much heat is needed to raise its temperature by 78 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1635 * 1.03 * 78.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=28.2 V and R=11.1 ohm.
Final: {"answer": 71.6432, "unit": "W"}

Answer: 71.6432

Prompt: A resistor has resistance 11.1 ohm and voltage 28.2 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=28.2 V and R=11.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=869.5 mg, t=273.5 h, and T_half=114 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 164.8396, "unit": "mg"}

Answer: 164.8396

Prompt: A radioactive sample starts with 869.5 mg. Its half-life is 114 hours. How many mg remain after 273.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=869.5 mg, t=273.5 h, and T_half=114 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.59 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 826.916, "unit": "g"}

Answer: 826.916

Prompt: A sample contains 4.59 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.59 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4285 mL to 4.285 L.
3. Compute M = 1.17 / 4.285.
Final: {"answer": 0.273, "unit": "mol/L"}

Answer: 0.273

Prompt: A solution contains 1.17 mol of solute in 4285 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4285 mL to 4.285 L.
Compute M = 1.17 / 4.285.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 13.9454, "unit": "state_units"}

Answer: 13.9454

Prompt: Use explicit Euler on dy/dt = -0.16 y with y(0)=55, step size h=1.5, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.1)=-42.76 and f(1.1)=-9.64.
3. The interval width is 7.2.
Final: {"answer": -188.64, "unit": "area_units"}

Answer: -188.64

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.6x+-14.7 from x=-6.1 to x=1.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.1)=-42.76 and f(1.1)=-9.64.
The interval width is 7.2.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [0.14, 0.161, 1.995], "unit": "temperature_units"}

Answer: 0.14

Answer: 0.161

Answer: 1.995

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=-1.7, right=1.75; current interior values are [-1.7, 2.3, 1.65]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -77.0 + 273.15.
Final: {"answer": 196.15, "unit": "K"}

Answer: 196.15

Prompt: Convert -77 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 -77.0 + 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=24 degrees and keep the unit as newtons.
Final: {"answer": [166.722, 74.2294], "unit": "N"}

Answer: 166.722

Answer: 74.2294

Prompt: A vector has magnitude 182.5 N at 24 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=24 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": [-5.45, -25.25], "unit": "dimensionless"}

Answer: -5.45

Answer: -25.25

Prompt: A line passes through points (15, -107) and (16.75, -116.538). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In lab notebook case 433650, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_001312(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_001312"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_001312(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

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

try:
    pairwise_ratios_001312([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_001312([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 8.45 kg and a = 10.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 87.4575, "unit": "N"}

Answer: 87.4575

Prompt: A cart has mass 8.45 kg and measured acceleration 10.35 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 = 8.45 kg and a = 10.35 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 = 26^2 and multiply by 0.5 * 13.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4394.0, "unit": "J"}

Answer: 4394.0

Prompt: A body of mass 13 kg moves at 26 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26^2 and multiply by 0.5 * 13.
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=71 degrees through the sine of 2 theta.
3. Substitute v=7.2 m/s and g=9.81 m/s^2.
Final: {"answer": 3.2534, "unit": "m"}

Answer: 3.2534

Prompt: A projectile is launched on level ground with no air resistance at speed 7.2 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=7.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.27 * 8.314 * 278 / 39.4.
Final: {"answer": 15.8388, "unit": "kPa"}

Answer: 15.8388

Prompt: An ideal gas sample has n=0.27 mol, T=278 K, and V=39.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.27 * 8.314 * 278 / 39.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1970 * 2.31 * 10.
Final: {"answer": 45507.0, "unit": "J"}

Answer: 45507.0

Prompt: A 1970 g sample has specific heat 2.31 J/(g*K). How much heat is needed to raise its temperature by 10 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1970 * 2.31 * 10.


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=39.5 V and R=195.7 ohm.
Final: {"answer": 7.9727, "unit": "W"}

Answer: 7.9727

Prompt: A resistor has resistance 195.7 ohm and voltage 39.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=39.5 V and R=195.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=587 mg, t=238 h, and T_half=116 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 141.5819, "unit": "mg"}

Answer: 141.5819

Prompt: A radioactive sample starts with 587 mg. Its half-life is 116 hours. How many mg remain after 238 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=587 mg, t=238 h, and T_half=116 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 355 mL to 0.355 L.
3. Compute M = 3.515 / 0.355.
Final: {"answer": 9.9014, "unit": "mol/L"}

Answer: 9.9014

Prompt: A solution contains 3.515 mol of solute in 355 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 355 mL to 0.355 L.
Compute M = 3.515 / 0.355.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0786, "unit": "state_units"}

Answer: 0.0786

Prompt: Use explicit Euler on dy/dt = -0.32 y with y(0)=22.5, step size h=1.35, 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) = -0.32 y, so each step multiplies y by 1 - h*0.32.
Apply that update for 10 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=0.46 and add it to the current value.
Final: {"answer": [1.22, 1.342, 0.944], "unit": "temperature_units"}

Answer: 1.22

Answer: 1.342

Answer: 0.944

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=2.1, right=1.9; current interior values are [2.6, 0.1, 0.3]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 123.5 + 273.15.
Final: {"answer": 396.65, "unit": "K"}

Answer: 396.65

Prompt: Convert 123.5 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 123.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=188 degrees and keep the unit as newtons.
Final: {"answer": [-403.5342, -56.713], "unit": "N"}

Answer: -403.5342

Answer: -56.713

Prompt: A vector has magnitude 407.5 N at 188 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=188 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In student derivation case 588466, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def finite_differences_001330(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_001330"}

Answer: python_code

Prompt: Write a Python function finite_differences_001330(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_001330([5]) == []

assert finite_differences_001330([]) == []


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 40.2 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=41 degrees through the sine of 2 theta.
3. Substitute v=42.9 m/s and g=9.81 m/s^2.
Final: {"answer": 185.7797, "unit": "m"}

Answer: 185.7797

Prompt: A projectile is launched on level ground with no air resistance at speed 42.9 m/s and angle 41 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=41 degrees through the sine of 2 theta.
Substitute v=42.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.1 * 8.314 * 340 / 1.0.
Final: {"answer": 3109.436, "unit": "kPa"}

Answer: 3109.436

Prompt: An ideal gas sample has n=1.1 mol, T=340 K, and V=1.0 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 = 1.1 * 8.314 * 340 / 1.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 405 * 3.905 * 63.
Final: {"answer": 99636.075, "unit": "J"}

Answer: 99636.075

Prompt: A 405 g sample has specific heat 3.905 J/(g*K). How much heat is needed to raise its temperature by 63 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 405 * 3.905 * 63.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=427 mg, t=244 h, and T_half=76 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 46.1278, "unit": "mg"}

Answer: 46.1278

Prompt: A radioactive sample starts with 427 mg. Its half-life is 76 hours. How many mg remain after 244 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=427 mg, t=244 h, and T_half=76 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 4620 mL to 4.62 L.
3. Compute M = 2.495 / 4.62.
Final: {"answer": 0.54, "unit": "mol/L"}

Answer: 0.54

Prompt: A solution contains 2.495 mol of solute in 4620 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4620 mL to 4.62 L.
Compute M = 2.495 / 4.62.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.52 y with y(0)=35, step size h=1.85, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4.1)=0.39 and f(-3.9)=1.01.
3. The interval width is 0.2.
Final: {"answer": 0.14, "unit": "area_units"}

Answer: 0.14

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.1x+13.1 from x=-4.1 to x=-3.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.1)=0.39 and f(-3.9)=1.01.
The interval width is 0.2.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 29830.0 / 1000.
Final: {"answer": 29.83, "unit": "kg"}

Answer: 29.83

Prompt: Convert 29830 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 29830.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=221 degrees and keep the unit as newtons.
Final: {"answer": [-81.1313, -70.5263], "unit": "N"}

Answer: -81.1313

Answer: -70.5263

Prompt: A vector has magnitude 107.5 N at 221 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=221 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [9.35, -24.0], "unit": "dimensionless"}

Answer: 9.35

Answer: -24.0

Prompt: A line passes through points (-10.5, -122.175) and (-1.5, -38.025). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In student derivation case 253873, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def clamp_001348(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_001348"}

Answer: python_code

Prompt: Write a Python function clamp_001348(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_001348(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=1.6 mol and T=292 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=84 degrees through the sine of 2 theta.
3. Substitute v=77.6 m/s and g=9.81 m/s^2.
Final: {"answer": 127.6243, "unit": "m"}

Answer: 127.6243

Prompt: A projectile is launched on level ground with no air resistance at speed 77.6 m/s and angle 84 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=84 degrees through the sine of 2 theta.
Substitute v=77.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.24 * 8.314 * 374 / 14.1.
Final: {"answer": 493.9813, "unit": "kPa"}

Answer: 493.9813

Prompt: An ideal gas sample has n=2.24 mol, T=374 K, and V=14.1 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 = 2.24 * 8.314 * 374 / 14.1.


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=62.1 V and R=99 ohm.
Final: {"answer": 38.9536, "unit": "W"}

Answer: 38.9536

Prompt: A resistor has resistance 99 ohm and voltage 62.1 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=62.1 V and R=99 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=303 mg, t=294.5 h, and T_half=28.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.2349, "unit": "mg"}

Answer: 0.2349

Prompt: A radioactive sample starts with 303 mg. Its half-life is 28.5 hours. How many mg remain after 294.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=303 mg, t=294.5 h, and T_half=28.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.84 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 151.331, "unit": "g"}

Answer: 151.331

Prompt: A sample contains 0.84 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.84 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1500 mL to 1.5 L.
3. Compute M = 1.795 / 1.5.
Final: {"answer": 1.1967, "unit": "mol/L"}

Answer: 1.1967

Prompt: A solution contains 1.795 mol of solute in 1500 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1500 mL to 1.5 L.
Compute M = 1.795 / 1.5.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.0513, "unit": "state_units"}

Answer: 0.0513

Prompt: Use explicit Euler on dy/dt = -0.62 y with y(0)=4.5, step size h=1.25, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.1)=63.73 and f(14)=121.4.
3. The interval width is 7.9.
Final: {"answer": 731.2635, "unit": "area_units"}

Answer: 731.2635

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+19.2 from x=6.1 to x=14. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.1)=63.73 and f(14)=121.4.
The interval width is 7.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [0.138, 1.22, 0.093], "unit": "temperature_units"}

Answer: 0.138

Answer: 1.22

Answer: 0.093

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=-0.2, right=-0.35; current interior values are [1.15, 0.3, 1.45]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=225 degrees and keep the unit as newtons.
Final: {"answer": [-7.4246, -7.4246], "unit": "N"}

Answer: -7.4246

Answer: -7.4246

Prompt: A vector has magnitude 10.5 N at 225 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=225 degrees and keep the unit as newtons.