  We present a new approach for obtaining very precise integration results for
infrared vertex and box diagrams, where the integration is carried out directly
without performing any analytic integration of Feynman parameters. Using an
appropriate numerical integration routine with an extrapolation method,
together with a multi-precision library, we have obtained integration results
which agree with the analytic results to 10 digits even for such a very small
photon mass as $10^{-150}$ GeV in the infrared vertex diagram.
