An objective of this article is to calculate continuous triple integrals numerically using the RS (RMS) method by applying Romberg acceleration to complex rules (the Simpson rule for the inner dimension x and the midpoint rule for the middle dimension y). The Simpson’s rules to outer dimensions z, denoted as symbol RS (RMS), where an inner dimension x is equal to the middle dimensions y and not equal to the outer dimensions z. We achieved high accuracy and a large number of sub-periods in a short time.