On Circle numerical computation of real definite integrals in Adaptive mode.

In the Cartesian two-dimensional space, this note applies a mixed quadrature rule in conjunction with an adaptive scheme across the circular surface. The two mathematical processes that result in a regular square area from the circular surface. The mixed quadrature rule was assessed in an adaptive scheme using five numerical tests. It was discovered to be more effective than Boole's rule. [ABSTRACT FROM AUTHOR]