Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [3.4, -25.5], "unit": "dimensionless"}

Answer: 3.4

Answer: -25.5

Prompt: A line passes through points (-11, -62.9) and (-5.25, -43.35). 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_001366(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_001366"}

Answer: python_code

Prompt: Write a Python function clamp_001366(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_001366(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=1.8 mol and T=451 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.15 kg and a = 9.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 65.065, "unit": "N"}

Answer: 65.065

Prompt: A cart has mass 7.15 kg and measured acceleration 9.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.15 kg and a = 9.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 25.45^2 and multiply by 0.5 * 15.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5019.6944, "unit": "J"}

Answer: 5019.6944

Prompt: A body of mass 15.5 kg moves at 25.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.45^2 and multiply by 0.5 * 15.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=26 degrees through the sine of 2 theta.
3. Substitute v=54.5 m/s and g=9.81 m/s^2.
Final: {"answer": 238.5921, "unit": "m"}

Answer: 238.5921

Prompt: A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 26 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=26 degrees through the sine of 2 theta.
Substitute v=54.5 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.76 * 8.314 * 584 / 114.5.
Final: {"answer": 159.4429, "unit": "kPa"}

Answer: 159.4429

Prompt: An ideal gas sample has n=3.76 mol, T=584 K, and V=114.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.76 * 8.314 * 584 / 114.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 225 * 3.045 * 84.
Final: {"answer": 57550.5, "unit": "J"}

Answer: 57550.5

Prompt: A 225 g sample has specific heat 3.045 J/(g*K). How much heat is needed to raise its temperature by 84 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 225 * 3.045 * 84.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.13 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 924.2003, "unit": "g"}

Answer: 924.2003

Prompt: A sample contains 5.13 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.13 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=42.5, step size h=1.55, 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) = -0.63 y, so each step multiplies y by 1 - h*0.63.
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(4.9)=34.18 and f(10.2)=56.44.
3. The interval width is 5.3.
Final: {"answer": 240.143, "unit": "area_units"}

Answer: 240.143

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.2x+13.6 from x=4.9 to x=10.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.9)=34.18 and f(10.2)=56.44.
The interval width is 5.3.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 170.0 + 273.15.
Final: {"answer": 443.15, "unit": "K"}

Answer: 443.15

Prompt: Convert 170 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 170.0 + 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=174 degrees and keep the unit as newtons.
Final: {"answer": [-247.636, 26.0276], "unit": "N"}

Answer: -247.636

Answer: 26.0276

Prompt: A vector has magnitude 249 N at 174 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=174 degrees and keep the unit as newtons.

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


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

Answer: inconsistent

Prompt: In quality-control check case 818887, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_001384(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_001384"}

Answer: python_code

Prompt: Write a Python function finite_differences_001384(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_001384([5]) == []

assert finite_differences_001384([]) == []


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.05 kg and a = 8.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 83.9175, "unit": "N"}

Answer: 83.9175

Prompt: A cart has mass 10.05 kg and measured acceleration 8.35 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 = 10.05 kg and a = 8.35 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 = 17.7^2 and multiply by 0.5 * 17.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2702.1262, "unit": "J"}

Answer: 2702.1262

Prompt: A body of mass 17.25 kg moves at 17.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.7^2 and multiply by 0.5 * 17.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.28 * 8.314 * 439 / 112.3.
Final: {"answer": 171.6045, "unit": "kPa"}

Answer: 171.6045

Prompt: An ideal gas sample has n=5.28 mol, T=439 K, and V=112.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.28 * 8.314 * 439 / 112.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 190 * 2.855 * 97.
Final: {"answer": 52617.65, "unit": "J"}

Answer: 52617.65

Prompt: A 190 g sample has specific heat 2.855 J/(g*K). How much heat is needed to raise its temperature by 97 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 190 * 2.855 * 97.


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=76.6 V and R=5.3 ohm.
Final: {"answer": 1107.0868, "unit": "W"}

Answer: 1107.0868

Prompt: A resistor has resistance 5.3 ohm and voltage 76.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=76.6 V and R=5.3 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4225 mL to 4.225 L.
3. Compute M = 2.52 / 4.225.
Final: {"answer": 0.5964, "unit": "mol/L"}

Answer: 0.5964

Prompt: A solution contains 2.52 mol of solute in 4225 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4225 mL to 4.225 L.
Compute M = 2.52 / 4.225.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 1.5331, "unit": "state_units"}

Answer: 1.5331

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=7.5, step size h=1.2, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.9)=-19.27 and f(-2.1)=-17.43.
3. The interval width is 0.8.
Final: {"answer": -14.68, "unit": "area_units"}

Answer: -14.68

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.3x+-12.6 from x=-2.9 to x=-2.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.9)=-19.27 and f(-2.1)=-17.43.
The interval width is 0.8.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=263 degrees and keep the unit as newtons.
Final: {"answer": [-18.8897, -153.8447], "unit": "N"}

Answer: -18.8897

Answer: -153.8447

Prompt: A vector has magnitude 155 N at 263 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=263 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [9.15, 29.75], "unit": "dimensionless"}

Answer: 9.15

Answer: 29.75

Prompt: A line passes through points (20, 212.75) and (28.5, 290.525). 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 165432, 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. 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)=42 and h=1.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.5 kg and a = 5.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 48.45, "unit": "N"}

Answer: 48.45

Prompt: A cart has mass 9.5 kg and measured acceleration 5.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.5 kg and a = 5.1 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 = 7^2 and multiply by 0.5 * 5.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 123.725, "unit": "J"}

Answer: 123.725

Prompt: A body of mass 5.05 kg moves at 7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7^2 and multiply by 0.5 * 5.05.
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=31 degrees through the sine of 2 theta.
3. Substitute v=73.9 m/s and g=9.81 m/s^2.
Final: {"answer": 491.5354, "unit": "m"}

Answer: 491.5354

Prompt: A projectile is launched on level ground with no air resistance at speed 73.9 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=31 degrees through the sine of 2 theta.
Substitute v=73.9 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 = 0.56 * 8.314 * 366 / 80.0.
Final: {"answer": 21.3005, "unit": "kPa"}

Answer: 21.3005

Prompt: An ideal gas sample has n=0.56 mol, T=366 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 = 0.56 * 8.314 * 366 / 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 = 510 * 3.395 * 66.
Final: {"answer": 114275.7, "unit": "J"}

Answer: 114275.7

Prompt: A 510 g sample has specific heat 3.395 J/(g*K). How much heat is needed to raise its temperature by 66 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 510 * 3.395 * 66.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=66.3 V and R=194.1 ohm.
Final: {"answer": 22.6465, "unit": "W"}

Answer: 22.6465

Prompt: A resistor has resistance 194.1 ohm and voltage 66.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=66.3 V and R=194.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=318 mg, t=308.5 h, and T_half=29.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.2261, "unit": "mg"}

Answer: 0.2261

Prompt: A radioactive sample starts with 318 mg. Its half-life is 29.5 hours. How many mg remain after 308.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=318 mg, t=308.5 h, and T_half=29.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3205 mL to 3.205 L.
3. Compute M = 0.165 / 3.205.
Final: {"answer": 0.0515, "unit": "mol/L"}

Answer: 0.0515

Prompt: A solution contains 0.165 mol of solute in 3205 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3205 mL to 3.205 L.
Compute M = 0.165 / 3.205.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.68 y with y(0)=57.5, step size h=1.4, 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) = -0.68 y, so each step multiplies y by 1 - h*0.68.
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(1.4)=-4.62 and f(7.1)=-46.23.
3. The interval width is 5.7.
Final: {"answer": -144.9225, "unit": "area_units"}

Answer: -144.9225

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.3x+5.6 from x=1.4 to x=7.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.4)=-4.62 and f(7.1)=-46.23.
The interval width is 5.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [0.824, 1.358, 0.08], "unit": "temperature_units"}

Answer: 0.824

Answer: 1.358

Answer: 0.08

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.1, right=-0.85; current interior values are [1.0, 0.5, 1.95]. Use r=0.44. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 10.5 + 273.15.
Final: {"answer": 283.65, "unit": "K"}

Answer: 283.65

Prompt: Convert 10.5 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 10.5 + 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=249 degrees and keep the unit as newtons.
Final: {"answer": [-129.3708, -337.0225], "unit": "N"}

Answer: -129.3708

Answer: -337.0225

Prompt: A vector has magnitude 361 N at 249 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=249 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": [-6.35, 20.25], "unit": "dimensionless"}

Answer: -6.35

Answer: 20.25

Prompt: A line passes through points (-6.5, 61.525) and (4.25, -6.7375). 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 222683, 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 clamp_001420(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_001420"}

Answer: python_code

Prompt: Write a Python function clamp_001420(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_001420(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: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a segmentation scoring problem with 1636 items and budget 74555, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.05 kg and a = 4.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 4.515, "unit": "N"}

Answer: 4.515

Prompt: A cart has mass 1.05 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.05 kg and a = 4.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.1^2 and multiply by 0.5 * 8.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2946.2333, "unit": "J"}

Answer: 2946.2333

Prompt: A body of mass 8.65 kg moves at 26.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.1^2 and multiply by 0.5 * 8.65.
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=65 degrees through the sine of 2 theta.
3. Substitute v=11.3 m/s and g=9.81 m/s^2.
Final: {"answer": 9.9711, "unit": "m"}

Answer: 9.9711

Prompt: A projectile is launched on level ground with no air resistance at speed 11.3 m/s and angle 65 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=65 degrees through the sine of 2 theta.
Substitute v=11.3 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 = 1800 * 0.69 * 118.
Final: {"answer": 146556.0, "unit": "J"}

Answer: 146556.0

Prompt: A 1800 g sample has specific heat 0.69 J/(g*K). How much heat is needed to raise its temperature by 118 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1800 * 0.69 * 118.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=160.2 V and R=93.7 ohm.
Final: {"answer": 273.8958, "unit": "W"}

Answer: 273.8958

Prompt: A resistor has resistance 93.7 ohm and voltage 160.2 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=160.2 V and R=93.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=127.5 mg, t=335.5 h, and T_half=63 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 3.1798, "unit": "mg"}

Answer: 3.1798

Prompt: A radioactive sample starts with 127.5 mg. Its half-life is 63 hours. How many mg remain after 335.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=127.5 mg, t=335.5 h, and T_half=63 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.6 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1008.8736, "unit": "g"}

Answer: 1008.8736

Prompt: A sample contains 5.6 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.6 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 3290 mL to 3.29 L.
3. Compute M = 3.31 / 3.29.
Final: {"answer": 1.0061, "unit": "mol/L"}

Answer: 1.0061

Prompt: A solution contains 3.31 mol of solute in 3290 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3290 mL to 3.29 L.
Compute M = 3.31 / 3.29.


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 2 steps and round the final state.
Final: {"answer": 53.6475, "unit": "state_units"}

Answer: 53.6475

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=64.5, step size h=1.1, 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) = -0.08 y, so each step multiplies y by 1 - h*0.08.
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(4.2)=-42.68 and f(13.5)=-111.5.
3. The interval width is 9.3.
Final: {"answer": -716.937, "unit": "area_units"}

Answer: -716.937

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+-11.6 from x=4.2 to x=13.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.2)=-42.68 and f(13.5)=-111.5.
The interval width is 9.3.


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=0.16 and add it to the current value.
Final: {"answer": [1.604, 0.994, -0.746], "unit": "temperature_units"}

Answer: 1.604

Answer: 0.994

Answer: -0.746

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=2.2, right=0.05; current interior values are [1.5, 1.45, -1.45]. Use r=0.16. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.16 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 38933.0 / 1000.
Final: {"answer": 38.933, "unit": "kg"}

Answer: 38.933

Prompt: Convert 38933 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 38933.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=310 degrees and keep the unit as newtons.
Final: {"answer": [190.2651, -226.7492], "unit": "N"}

Answer: 190.2651

Answer: -226.7492

Prompt: A vector has magnitude 296 N at 310 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=310 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": [10.0, 3.0], "unit": "dimensionless"}

Answer: 10.0

Answer: 3.0

Prompt: A line passes through points (-19.75, -194.5) and (-11, -107). 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 simulation spec case 594470, 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_001438(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_001438"}

Answer: python_code

Prompt: Write a Python function threshold_flags_001438(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_001438([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_001438([], 5) == []

assert threshold_flags_001438([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=21 and h=0.05, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 5.5^2 and multiply by 0.5 * 0.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9.075, "unit": "J"}

Answer: 9.075

Prompt: A body of mass 0.6 kg moves at 5.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.5^2 and multiply by 0.5 * 0.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=13 degrees through the sine of 2 theta.
3. Substitute v=40.1 m/s and g=9.81 m/s^2.
Final: {"answer": 71.8558, "unit": "m"}

Answer: 71.8558

Prompt: A projectile is launched on level ground with no air resistance at speed 40.1 m/s and angle 13 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=13 degrees through the sine of 2 theta.
Substitute v=40.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.51 * 8.314 * 558 / 34.8.
Final: {"answer": 467.9205, "unit": "kPa"}

Answer: 467.9205

Prompt: An ideal gas sample has n=3.51 mol, T=558 K, and V=34.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.51 * 8.314 * 558 / 34.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1880 * 3.63 * 75.
Final: {"answer": 511830.0, "unit": "J"}

Answer: 511830.0

Prompt: A 1880 g sample has specific heat 3.63 J/(g*K). How much heat is needed to raise its temperature by 75 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1880 * 3.63 * 75.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=145.2 V and R=26.4 ohm.
Final: {"answer": 798.6, "unit": "W"}

Answer: 798.6

Prompt: A resistor has resistance 26.4 ohm and voltage 145.2 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=145.2 V and R=26.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=251 mg, t=313 h, and T_half=105.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 32.1048, "unit": "mg"}

Answer: 32.1048

Prompt: A radioactive sample starts with 251 mg. Its half-life is 105.5 hours. How many mg remain after 313 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=251 mg, t=313 h, and T_half=105.5 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 = 2.41 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 241.2097, "unit": "g"}

Answer: 241.2097

Prompt: A sample contains 2.41 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 = 2.41 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 4485 mL to 4.485 L.
3. Compute M = 4.085 / 4.485.
Final: {"answer": 0.9108, "unit": "mol/L"}

Answer: 0.9108

Prompt: A solution contains 4.085 mol of solute in 4485 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4485 mL to 4.485 L.
Compute M = 4.085 / 4.485.


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 2 steps and round the final state.
Final: {"answer": 3.7798, "unit": "state_units"}

Answer: 3.7798

Prompt: Use explicit Euler on dy/dt = -0.57 y with y(0)=5.5, step size h=0.3, 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) = -0.57 y, so each step multiplies y by 1 - h*0.57.
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(-0.2)=-17.34 and f(3.4)=-14.82.
3. The interval width is 3.6.
Final: {"answer": -57.888, "unit": "area_units"}

Answer: -57.888

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+-17.2 from x=-0.2 to x=3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.2)=-17.34 and f(3.4)=-14.82.
The interval width is 3.6.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -55.5 + 273.15.
Final: {"answer": 217.65, "unit": "K"}

Answer: 217.65

Prompt: Convert -55.5 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 -55.5 + 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=124 degrees and keep the unit as newtons.
Final: {"answer": [-95.3424, 141.3509], "unit": "N"}

Answer: -95.3424

Answer: 141.3509

Prompt: A vector has magnitude 170.5 N at 124 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=124 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 703693, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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 35.4 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 = 4.35 kg and a = 12.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.4175, "unit": "N"}

Answer: 52.4175

Prompt: A cart has mass 4.35 kg and measured acceleration 12.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.35 kg and a = 12.05 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 = 5.4^2 and multiply by 0.5 * 8.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 123.201, "unit": "J"}

Answer: 123.201

Prompt: A body of mass 8.45 kg moves at 5.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.4^2 and multiply by 0.5 * 8.45.
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=77 degrees through the sine of 2 theta.
3. Substitute v=9.4 m/s and g=9.81 m/s^2.
Final: {"answer": 3.9485, "unit": "m"}

Answer: 3.9485

Prompt: A projectile is launched on level ground with no air resistance at speed 9.4 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=9.4 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 = 4.33 * 8.314 * 489 / 102.8.
Final: {"answer": 171.2433, "unit": "kPa"}

Answer: 171.2433

Prompt: An ideal gas sample has n=4.33 mol, T=489 K, and V=102.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.33 * 8.314 * 489 / 102.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 560 * 2 * 7.
Final: {"answer": 7840.0, "unit": "J"}

Answer: 7840.0

Prompt: A 560 g sample has specific heat 2 J/(g*K). How much heat is needed to raise its temperature by 7 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 560 * 2 * 7.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=635 mg, t=249.5 h, and T_half=58 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 32.1978, "unit": "mg"}

Answer: 32.1978

Prompt: A radioactive sample starts with 635 mg. Its half-life is 58 hours. How many mg remain after 249.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=635 mg, t=249.5 h, and T_half=58 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 1570 mL to 1.57 L.
3. Compute M = 1.91 / 1.57.
Final: {"answer": 1.2166, "unit": "mol/L"}

Answer: 1.2166

Prompt: A solution contains 1.91 mol of solute in 1570 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1570 mL to 1.57 L.
Compute M = 1.91 / 1.57.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-0.8)=-0.5 and f(7.3)=64.3.
3. The interval width is 8.1.
Final: {"answer": 258.39, "unit": "area_units"}

Answer: 258.39

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=8x+5.9 from x=-0.8 to x=7.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.8)=-0.5 and f(7.3)=64.3.
The interval width is 8.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [0.884, 0.04, 0.946], "unit": "temperature_units"}

Answer: 0.884

Answer: 0.04

Answer: 0.946

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=2.85; current interior values are [-0.3, 1.4, -1.15]. Use r=0.32. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4955.5 / 100.
Final: {"answer": 49.555, "unit": "m"}

Answer: 49.555

Prompt: Convert 4955.5 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 4955.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=169 degrees and keep the unit as newtons.
Final: {"answer": [-199.2703, 38.7342], "unit": "N"}

Answer: -199.2703

Answer: 38.7342

Prompt: A vector has magnitude 203 N at 169 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=169 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.0, 7.5], "unit": "dimensionless"}

Answer: -2.0

Answer: 7.5

Prompt: A line passes through points (7.25, -7) and (21.5, -35.5). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 314779, 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 running_total_001474(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_001474"}

Answer: python_code

Prompt: Write a Python function running_total_001474(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: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a knapsack scoring problem with 3288 items and budget 70450, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 20.45^2 and multiply by 0.5 * 14.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3126.0637, "unit": "J"}

Answer: 3126.0637

Prompt: A body of mass 14.95 kg moves at 20.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 20.45^2 and multiply by 0.5 * 14.95.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=76 degrees through the sine of 2 theta.
3. Substitute v=54.5 m/s and g=9.81 m/s^2.
Final: {"answer": 142.1456, "unit": "m"}

Answer: 142.1456

Prompt: A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=76 degrees through the sine of 2 theta.
Substitute v=54.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1710 * 4.305 * 83.
Final: {"answer": 611008.65, "unit": "J"}

Answer: 611008.65

Prompt: A 1710 g sample has specific heat 4.305 J/(g*K). How much heat is needed to raise its temperature by 83 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1710 * 4.305 * 83.


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=27.8 V and R=92.7 ohm.
Final: {"answer": 8.337, "unit": "W"}

Answer: 8.337

Prompt: A resistor has resistance 92.7 ohm and voltage 27.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=27.8 V and R=92.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=757 mg, t=163 h, and T_half=74.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 166.137, "unit": "mg"}

Answer: 166.137

Prompt: A radioactive sample starts with 757 mg. Its half-life is 74.5 hours. How many mg remain after 163 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=757 mg, t=163 h, and T_half=74.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.3 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 774.6708, "unit": "g"}

Answer: 774.6708

Prompt: A sample contains 4.3 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 = 4.3 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 1645 mL to 1.645 L.
3. Compute M = 1.085 / 1.645.
Final: {"answer": 0.6596, "unit": "mol/L"}

Answer: 0.6596

Prompt: A solution contains 1.085 mol of solute in 1645 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1645 mL to 1.645 L.
Compute M = 1.085 / 1.645.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.33 y, so each step multiplies y by 1 - h*0.33.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 6.035, "unit": "state_units"}

Answer: 6.035

Prompt: Use explicit Euler on dy/dt = -0.33 y with y(0)=43.5, step size h=0.85, 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) = -0.33 y, so each step multiplies y by 1 - h*0.33.
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(4.9)=44.11 and f(6.5)=55.15.
3. The interval width is 1.6.
Final: {"answer": 79.408, "unit": "area_units"}

Answer: 79.408

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.9x+10.3 from x=4.9 to x=6.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.9)=44.11 and f(6.5)=55.15.
The interval width is 1.6.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 625.5 / 100.
Final: {"answer": 6.255, "unit": "m"}

Answer: 6.255

Prompt: Convert 625.5 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 625.5 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.9, -19.75], "unit": "dimensionless"}

Answer: 6.9

Answer: -19.75

Prompt: A line passes through points (-13.5, -112.9) and (-2.5, -37). 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 simulation spec case 170831, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each field ledger record from batch 650512 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.85 kg and a = 2.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 45.87, "unit": "N"}

Answer: 45.87

Prompt: A cart has mass 20.85 kg and measured acceleration 2.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.85 kg and a = 2.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 27.15^2 and multiply by 0.5 * 3.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1308.3924, "unit": "J"}

Answer: 1308.3924

Prompt: A body of mass 3.55 kg moves at 27.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 27.15^2 and multiply by 0.5 * 3.55.
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=75 degrees through the sine of 2 theta.
3. Substitute v=55.2 m/s and g=9.81 m/s^2.
Final: {"answer": 155.3028, "unit": "m"}

Answer: 155.3028

Prompt: A projectile is launched on level ground with no air resistance at speed 55.2 m/s and angle 75 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=75 degrees through the sine of 2 theta.
Substitute v=55.2 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 = 3.92 * 8.314 * 530 / 70.8.
Final: {"answer": 243.9713, "unit": "kPa"}

Answer: 243.9713

Prompt: An ideal gas sample has n=3.92 mol, T=530 K, and V=70.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.92 * 8.314 * 530 / 70.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1400 * 3.765 * 80.
Final: {"answer": 421680.0, "unit": "J"}

Answer: 421680.0

Prompt: A 1400 g sample has specific heat 3.765 J/(g*K). How much heat is needed to raise its temperature by 80 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1400 * 3.765 * 80.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=77 mg, t=267 h, and T_half=105.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 13.3242, "unit": "mg"}

Answer: 13.3242

Prompt: A radioactive sample starts with 77 mg. Its half-life is 105.5 hours. How many mg remain after 267 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=77 mg, t=267 h, and T_half=105.5 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 = 2.54 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 457.5962, "unit": "g"}

Answer: 457.5962

Prompt: A sample contains 2.54 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 = 2.54 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 4550 mL to 4.55 L.
3. Compute M = 3.1 / 4.55.
Final: {"answer": 0.6813, "unit": "mol/L"}

Answer: 0.6813

Prompt: A solution contains 3.1 mol of solute in 4550 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4550 mL to 4.55 L.
Compute M = 3.1 / 4.55.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0016, "unit": "state_units"}

Answer: 0.0016

Prompt: Use explicit Euler on dy/dt = -0.71 y with y(0)=39.5, step size h=0.95, 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) = -0.71 y, so each step multiplies y by 1 - h*0.71.
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(9.6)=58.86 and f(15.5)=88.95.
3. The interval width is 5.9.
Final: {"answer": 436.0395, "unit": "area_units"}

Answer: 436.0395

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.1x+9.9 from x=9.6 to x=15.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.6)=58.86 and f(15.5)=88.95.
The interval width is 5.9.


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=0.12 and add it to the current value.
Final: {"answer": [0.614, 2.028, -0.908], "unit": "temperature_units"}

Answer: 0.614

Answer: 2.028

Answer: -0.908

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=2.75, right=2.1; current interior values are [-0.1, 3.0, -2.0]. Use r=0.12. 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=0.12 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 4665.5 / 100.
Final: {"answer": 46.655, "unit": "m"}

Answer: 46.655

Prompt: Convert 4665.5 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 4665.5 / 100.


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

Answer: inconsistent

Prompt: In field worksheet case 391081, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. 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=78 m/s and g=9.81 m/s^2.
Final: {"answer": 557.4172, "unit": "m"}

Answer: 557.4172

Prompt: A projectile is launched on level ground with no air resistance at speed 78 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=78 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 = 0.53 * 8.314 * 302 / 104.6.
Final: {"answer": 12.7222, "unit": "kPa"}

Answer: 12.7222

Prompt: An ideal gas sample has n=0.53 mol, T=302 K, and V=104.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.53 * 8.314 * 302 / 104.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 730 * 2.375 * 11.
Final: {"answer": 19071.25, "unit": "J"}

Answer: 19071.25

Prompt: A 730 g sample has specific heat 2.375 J/(g*K). How much heat is needed to raise its temperature by 11 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 730 * 2.375 * 11.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=49 mg, t=303.5 h, and T_half=117.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 8.1779, "unit": "mg"}

Answer: 8.1779

Prompt: A radioactive sample starts with 49 mg. Its half-life is 117.5 hours. How many mg remain after 303.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=49 mg, t=303.5 h, and T_half=117.5 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 = 5.78 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 337.7832, "unit": "g"}

Answer: 337.7832

Prompt: A sample contains 5.78 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.78 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 365 mL to 0.365 L.
3. Compute M = 3.375 / 0.365.
Final: {"answer": 9.2466, "unit": "mol/L"}

Answer: 9.2466

Prompt: A solution contains 3.375 mol of solute in 365 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 365 mL to 0.365 L.
Compute M = 3.375 / 0.365.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.7)=20.71 and f(-0.7)=15.41.
3. The interval width is 1.
Final: {"answer": 18.06, "unit": "area_units"}

Answer: 18.06

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.3x+11.7 from x=-1.7 to x=-0.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.7)=20.71 and f(-0.7)=15.41.
The interval width is 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=0.34 and add it to the current value.
Final: {"answer": [0.894, 0.613, 1.191], "unit": "temperature_units"}

Answer: 0.894

Answer: 0.613

Answer: 1.191

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=1.85; current interior values are [0.35, 2.5, -0.9]. Use r=0.34. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=214 degrees and keep the unit as newtons.
Final: {"answer": [-310.4746, -209.4177], "unit": "N"}

Answer: -310.4746

Answer: -209.4177

Prompt: A vector has magnitude 374.5 N at 214 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=214 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 field worksheet case 722344, 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 normalize_001528(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_001528"}

Answer: python_code

Prompt: Write a Python function normalize_001528(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_001528([2, 3, 5]); assert len(out) == 3

try:
    normalize_001528([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 experiment records in release 963052, 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 = 3 kg and a = 12.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 37.95, "unit": "N"}

Answer: 37.95

Prompt: A cart has mass 3 kg and measured acceleration 12.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3 kg and a = 12.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 4.2^2 and multiply by 0.5 * 11.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 100.107, "unit": "J"}

Answer: 100.107

Prompt: A body of mass 11.35 kg moves at 4.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 4.2^2 and multiply by 0.5 * 11.35.
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=28 degrees through the sine of 2 theta.
3. Substitute v=43.1 m/s and g=9.81 m/s^2.
Final: {"answer": 156.9856, "unit": "m"}

Answer: 156.9856

Prompt: A projectile is launched on level ground with no air resistance at speed 43.1 m/s and angle 28 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=28 degrees through the sine of 2 theta.
Substitute v=43.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.77 * 8.314 * 360 / 76.1.
Final: {"answer": 69.6147, "unit": "kPa"}

Answer: 69.6147

Prompt: An ideal gas sample has n=1.77 mol, T=360 K, and V=76.1 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 = 1.77 * 8.314 * 360 / 76.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 40 * 3.355 * 35.
Final: {"answer": 4697.0, "unit": "J"}

Answer: 4697.0

Prompt: A 40 g sample has specific heat 3.355 J/(g*K). How much heat is needed to raise its temperature by 35 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 40 * 3.355 * 35.


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=20 V and R=148.3 ohm.
Final: {"answer": 2.6972, "unit": "W"}

Answer: 2.6972

Prompt: A resistor has resistance 148.3 ohm and voltage 20 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=20 V and R=148.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=345.5 mg, t=360 h, and T_half=60 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 5.3984, "unit": "mg"}

Answer: 5.3984

Prompt: A radioactive sample starts with 345.5 mg. Its half-life is 60 hours. How many mg remain after 360 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=345.5 mg, t=360 h, and T_half=60 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 = 2.89 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 127.1889, "unit": "g"}

Answer: 127.1889

Prompt: A sample contains 2.89 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.89 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 450 mL to 0.45 L.
3. Compute M = 2.885 / 0.45.
Final: {"answer": 6.4111, "unit": "mol/L"}

Answer: 6.4111

Prompt: A solution contains 2.885 mol of solute in 450 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 450 mL to 0.45 L.
Compute M = 2.885 / 0.45.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0337, "unit": "state_units"}

Answer: 0.0337

Prompt: Use explicit Euler on dy/dt = -0.4 y with y(0)=79.5, 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) = -0.4 y, so each step multiplies y by 1 - h*0.4.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-3.7)=-19.55 and f(3.8)=-15.8.
3. The interval width is 7.5.
Final: {"answer": -132.5625, "unit": "area_units"}

Answer: -132.5625

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.5x+-17.7 from x=-3.7 to x=3.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.7)=-19.55 and f(3.8)=-15.8.
The interval width is 7.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.2 and add it to the current value.
Final: {"answer": [0.0, 1.12, -0.31], "unit": "temperature_units"}

Answer: 0.0

Answer: 1.12

Answer: -0.31

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-0.55; current interior values are [-0.6, 2.45, -1.15]. Use r=0.2. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 11.0 + 273.15.
Final: {"answer": 284.15, "unit": "K"}

Answer: 284.15

Prompt: Convert 11 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 11.0 + 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=33 degrees and keep the unit as newtons.
Final: {"answer": [132.0906, 85.7806], "unit": "N"}

Answer: 132.0906

Answer: 85.7806

Prompt: A vector has magnitude 157.5 N at 33 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=33 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.05, -11.5], "unit": "dimensionless"}

Answer: 4.05

Answer: -11.5

Prompt: A line passes through points (-7.25, -40.8625) and (2, -3.4). 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 finite_differences_001546(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_001546"}

Answer: python_code

Prompt: Write a Python function finite_differences_001546(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_001546([5]) == []

assert finite_differences_001546([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid field survey records in release 350122, 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 = 12.05 kg and a = 12.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 151.2275, "unit": "N"}

Answer: 151.2275

Prompt: A cart has mass 12.05 kg and measured acceleration 12.55 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 = 12.05 kg and a = 12.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.92 * 8.314 * 603 / 41.7.
Final: {"answer": 591.5022, "unit": "kPa"}

Answer: 591.5022

Prompt: An ideal gas sample has n=4.92 mol, T=603 K, and V=41.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.92 * 8.314 * 603 / 41.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 155 * 1.12 * 73.
Final: {"answer": 12672.8, "unit": "J"}

Answer: 12672.8

Prompt: A 155 g sample has specific heat 1.12 J/(g*K). How much heat is needed to raise its temperature by 73 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 155 * 1.12 * 73.


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=88.5 V and R=23.7 ohm.
Final: {"answer": 330.4747, "unit": "W"}

Answer: 330.4747

Prompt: A resistor has resistance 23.7 ohm and voltage 88.5 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=88.5 V and R=23.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=932 mg, t=218.5 h, and T_half=101.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 209.5974, "unit": "mg"}

Answer: 209.5974

Prompt: A radioactive sample starts with 932 mg. Its half-life is 101.5 hours. How many mg remain after 218.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=932 mg, t=218.5 h, and T_half=101.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.16 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 416.3619, "unit": "g"}

Answer: 416.3619

Prompt: A sample contains 4.16 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.16 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 2595 mL to 2.595 L.
3. Compute M = 4.925 / 2.595.
Final: {"answer": 1.8979, "unit": "mol/L"}

Answer: 1.8979

Prompt: A solution contains 4.925 mol of solute in 2595 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2595 mL to 2.595 L.
Compute M = 4.925 / 2.595.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 2.5062, "unit": "state_units"}

Answer: 2.5062

Prompt: Use explicit Euler on dy/dt = -0.94 y with y(0)=12, step size h=1.55, 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) = -0.94 y, so each step multiplies y by 1 - h*0.94.
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(3.1)=17.34 and f(7.5)=32.3.
3. The interval width is 4.4.
Final: {"answer": 109.208, "unit": "area_units"}

Answer: 109.208

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.4x+6.8 from x=3.1 to x=7.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.1)=17.34 and f(7.5)=32.3.
The interval width is 4.4.


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=0.18 and add it to the current value.
Final: {"answer": [0.636, -0.669, -0.914], "unit": "temperature_units"}

Answer: 0.636

Answer: -0.669

Answer: -0.914

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.6, right=-0.5; current interior values are [1.5, -1.2, -0.95]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 175.0 + 273.15.
Final: {"answer": 448.15, "unit": "K"}

Answer: 448.15

Prompt: Convert 175 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 175.0 + 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=50 degrees and keep the unit as newtons.
Final: {"answer": [118.5943, 141.3352], "unit": "N"}

Answer: 118.5943

Answer: 141.3352

Prompt: A vector has magnitude 184.5 N at 50 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=50 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.15, 9.25], "unit": "dimensionless"}

Answer: 7.15

Answer: 9.25

Prompt: A line passes through points (-4.25, -21.1375) and (6.25, 53.9375). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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 simulation spec case 199215, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def finite_differences_001564(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_001564"}

Answer: python_code

Prompt: Write a Python function finite_differences_001564(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_001564([5]) == []

assert finite_differences_001564([]) == []


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=0.4 and interior values [2.9, -1.55, 1.85], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15 kg and a = 14.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 219.75, "unit": "N"}

Answer: 219.75

Prompt: A cart has mass 15 kg and measured acceleration 14.65 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 = 15 kg and a = 14.65 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 = 5.85^2 and multiply by 0.5 * 16.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 278.0578, "unit": "J"}

Answer: 278.0578

Prompt: A body of mass 16.25 kg moves at 5.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.85^2 and multiply by 0.5 * 16.25.
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=75 degrees through the sine of 2 theta.
3. Substitute v=18.5 m/s and g=9.81 m/s^2.
Final: {"answer": 17.4439, "unit": "m"}

Answer: 17.4439

Prompt: A projectile is launched on level ground with no air resistance at speed 18.5 m/s and angle 75 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=75 degrees through the sine of 2 theta.
Substitute v=18.5 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 = 3.76 * 8.314 * 471 / 113.0.
Final: {"answer": 130.2988, "unit": "kPa"}

Answer: 130.2988

Prompt: An ideal gas sample has n=3.76 mol, T=471 K, and V=113.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.76 * 8.314 * 471 / 113.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1215 * 1.825 * 10.
Final: {"answer": 22173.75, "unit": "J"}

Answer: 22173.75

Prompt: A 1215 g sample has specific heat 1.825 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 = 1215 * 1.825 * 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=23.6 V and R=189.1 ohm.
Final: {"answer": 2.9453, "unit": "W"}

Answer: 2.9453

Prompt: A resistor has resistance 189.1 ohm and voltage 23.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=23.6 V and R=189.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=604.5 mg, t=311.5 h, and T_half=47 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 6.1132, "unit": "mg"}

Answer: 6.1132

Prompt: A radioactive sample starts with 604.5 mg. Its half-life is 47 hours. How many mg remain after 311.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=604.5 mg, t=311.5 h, and T_half=47 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.05 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 189.1638, "unit": "g"}

Answer: 189.1638

Prompt: A sample contains 1.05 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 = 1.05 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 840 mL to 0.84 L.
3. Compute M = 0.895 / 0.84.
Final: {"answer": 1.0655, "unit": "mol/L"}

Answer: 1.0655

Prompt: A solution contains 0.895 mol of solute in 840 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 840 mL to 0.84 L.
Compute M = 0.895 / 0.84.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 1.7835, "unit": "state_units"}

Answer: 1.7835

Prompt: Use explicit Euler on dy/dt = -0.54 y with y(0)=41.5, step size h=0.5, 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) = -0.54 y, so each step multiplies y by 1 - h*0.54.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.7)=0.86 and f(3.6)=5.18.
3. The interval width is 0.9.
Final: {"answer": 2.718, "unit": "area_units"}

Answer: 2.718

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-12.1 from x=2.7 to x=3.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.7)=0.86 and f(3.6)=5.18.
The interval width is 0.9.


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=0.36 and add it to the current value.
Final: {"answer": [0.814, -0.458, -0.932], "unit": "temperature_units"}

Answer: 0.814

Answer: -0.458

Answer: -0.932

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=2.65, right=-1.5; current interior values are [-0.05, -0.35, -0.95]. Use r=0.36. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 80.0 + 273.15.
Final: {"answer": 353.15, "unit": "K"}

Answer: 353.15

Prompt: Convert 80 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 80.0 + 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=140 degrees and keep the unit as newtons.
Final: {"answer": [-366.9353, 307.8953], "unit": "N"}

Answer: -366.9353

Answer: 307.8953

Prompt: A vector has magnitude 479 N at 140 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=140 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.3, 1.5], "unit": "dimensionless"}

Answer: 4.3

Answer: 1.5

Prompt: A line passes through points (-6.25, -25.375) and (-3, -11.4). 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. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In instrument manual case 417247, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.06 and interior values [-1.35, 1.2, -0.75], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.35 kg and a = 0.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 4.0425, "unit": "N"}

Answer: 4.0425

Prompt: A cart has mass 7.35 kg and measured acceleration 0.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.35 kg and a = 0.55 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 = 21.45^2 and multiply by 0.5 * 16.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3761.3379, "unit": "J"}

Answer: 3761.3379

Prompt: A body of mass 16.35 kg moves at 21.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.45^2 and multiply by 0.5 * 16.35.
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=67 degrees through the sine of 2 theta.
3. Substitute v=73.5 m/s and g=9.81 m/s^2.
Final: {"answer": 396.1318, "unit": "m"}

Answer: 396.1318

Prompt: A projectile is launched on level ground with no air resistance at speed 73.5 m/s and angle 67 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=67 degrees through the sine of 2 theta.
Substitute v=73.5 m/s and g=9.81 m/s^2.