a = (v − v₀) / t — average acceleration from change in velocity over time.

Convert between degrees and radians: rad = deg × π/180.

Find the length of a circular arc: s = r × θ (θ in radians).

Find the nth term of an arithmetic sequence: aₙ = a₁ + (n−1)·d.

Sum the first n terms of an arithmetic sequence: Sₙ = n/2 · (a₁ + aₙ).

P(A|B) = P(B|A) · P(A) / P(B).

Probability of exactly k successes in n independent trials: P = C(n,k)·pᵏ·(1−p)^(n−k).

Compute the binomial coefficient C(n, k) = n! / (k! · (n−k)!).

Differentiate and integrate any function — the engine's `derivative()` and `integral()` return results you can graph and evaluate.

Find the area of a circle from its radius: A = π × r².

Find the circumference of a circle from its radius: C = 2 × π × r.

Convert ax² + bx + c into a(x − h)² + k form.

Compute P(A|B) = P(A ∩ B) / P(B).

Find the surface area of a cone (lateral + base).

Find the volume of a cone: V = (1/3) × π × r² × h.

Compute the population covariance of two 5-point datasets: cov(X,Y) = Σ(xᵢ−x̄)(yᵢ−ȳ) / n.

Find the volume and surface area of a cube from its side length.

Find the total surface area of a closed cylinder: A = 2πr(r + h).

Find the volume of a cylinder: V = π × r² × h.

Evaluate ∫ₐᵇ c·xⁿ dx = c·(b^(n+1) − a^(n+1))/(n+1).

Evaluate (f∘g)'(x) = f'(g(x)) · g'(x).

Evaluate d/dx [a·xⁿ] = a·n·x^(n−1) at a given point.

Evaluate (f·g)' = f'·g + f·g' at a given x using user-supplied f, g, f', g'.

Compute the discriminant b² − 4ac of a quadratic.