Simpson's Method is usually faster simply because you usually don't need to evaluate the function at as many points to obtain the same accuracy for the definite integral. If you are integrating smooth functions both are reliable. If your function may have some regions of rapid change in value and derivatives, then trapezoidal is more reliable.

The Trapezoid Rule is nothing more than the average of the left-hand and right-hand Riemann Sums. It provides a more accurate approximation of total change than either sum does alone. Simpson's Rule is a weighted average that results in an even more accurate approximation.

Dear Dr. @Jumah Aswad Zarnan

The Simpson method is the best of the trapezoidal method because the Simpson method needs more dividing points than the trapezoidal method. According to numerical methods, the greater the number of divisions, the better the solution.