/**
 * Performs adaptive Simpson's rule for numerical integration.
 * @param f - The function to integrate.
 * @param a - The lower limit of integration.
 * @param b - The upper limit of integration.
 * @param eps - The tolerance/accuracy desired.
 * @param depth - The maximum recursion depth.
 * @returns The approximate integral of the function from a to b.
 */
export declare function adaptiveSimpson(f: (y: number) => number, a: number, b: number, eps: number, depth: number): number;
/**
 * Root finding using bisection method.
 * @param f - The function whose root is sought.
 * @param a - The lower bound of the interval.
 * @param b - The upper bound of the interval.
 * @param eps - The tolerance/accuracy desired.
 * @returns A root of the function f within the interval [a, b].
 */
export declare function bisection(f: (x: number) => number, a: number, b: number, eps?: number): number;
/**
 * Root finding using the secant method.
 * @param f - The function whose root is sought.
 * @param a - An initial approximation to the root.
 * @param b - Another initial approximation to the root.
 * @param eps - The tolerance/accuracy desired.
 * @returns An approximation to a root of the function f.
 */
export declare function secant(f: (x: number) => number, a: number, b: number, eps?: number): number;
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