  We investigate the use of conformal maps for the acceleration of convergence
of the trapezoidal rule and Sinc numerical methods. The conformal map is a
polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite
number of singularities in the complex plane. In the case where locations are
unknown, the so-called Sinc-Pad\'e approximants are used to provide approximate
results. This adaptive method is shown to have almost the same convergence
properties. We use the conformal maps to generate high accuracy solutions to
several challenging integrals, nonlinear waves, and multidimensional integrals.
