In this paper, we started with the simplest method of numerical integration based on interpolation using the Maple package. We demonstrate some of the computational capabilities of the Maple package using the Newton– Coates formula for numerical integration. Newton –Coates formula is a very useful and simple family of generalized integral methods. The Trapezoidal method and the Simpson method can be accurately represented by the Maple package. For numerical integration and geometric analysis, the Maple is the best option. Considering a function f defined in the interval [a, b], we can draw an interpolation polynomial at some point f (x) with the Maple packet. Since it is simple to evaluate the definite integral of a polynomial, this calculation can be used to approximate the integral of . This is the Newton – Cotes approach to approximating integrals.