  Approximating a definite integral of product of cosines to within an accuracy
of n binary digits where the integrand depends on input integers x[k] given in
binary radix, is equivalent to counting the number of equal-sum partitions of
the integers and is thus a #P problem. Similarly, integrating this function
from zero to infinity and deciding whether the result is either zero or
infinity is an NP-Complete problem. Efficient numerical integration methods
such as the double exponential formula and the sinc approximation have been
around since the mid 70's. Noting the hardness of approximating the integral we
argue that the proven rates of convergence of such methods cannot possibly be
correct since they give rise to an anomalous result as P=#P.
