Numerical Integration Function | Dataford Interview Questions

U.S. Bank National Association analyzes sampled risk and pricing curves whose exact integrals may not be available in closed form. Implement composite Simpson's rule to approximate the definite integral of a curve from a to b.

Formal Specification

Write integrate_simpson(values, a, b, n), where values is an array of n + 1 numeric samples. The samples are ordered from left to right and represent f(a + i * h), where h = (b - a) / n. Return the numerical approximation as a floating-point number.

Composite Simpson's rule is:

integral = (h / 3) * (f(a) + f(b) + 4 * sum(odd-indexed samples) + 2 * sum(even-indexed interior samples))

Constraints

2 <= n <= 10^6
n is even
len(values) == n + 1
a < b
Sample values are finite numbers in [-10^9, 10^9]

Function Signature

def integrate_simpson(values, a, b, n):

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