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In this paper, a new modified algorithm is designed for combined numerical integration. Using the modified algorithm several definite integrals have been approximated, and the results have been compared with existing rules and a rule proposed by(Md. Amanat Ullah, 2015).The rules from the closed quadrature family, namely, Trapezoidal rule, Simpson’s 1/3rule and Weddle’s rule have been used. The results obtained by combined use of these quadrature rules as per the proposed algorithm show that the new modified algorithm gives more accuracy when compared with existing rules and the rule of Md. Amanat Ullah for a fixed number of intervals.