QTRAP

       Integrate using trapezoidal rule to specified accuracy.

       Integrate a function to specified accuracy using the extended
       trapezoidal rule.   Adapted from Numerical Recipes (1992, 2nd edition),
       Section 4.2.

       QTRAP, func, A, B, S, [EPS = , MAX_ITER =, _EXTRA = ]

       func - scalar string giving name of function of one variable to
               be integrated
       A,B  - numeric scalars giving the lower and upper bound of the
               integration

       S - Scalar giving the approximation to the integral of the specified
               function between A and B.

       EPS - scalar specify the fractional accuracy before ending the
             iteration.    Default = 1E-6
       MAX_ITER - Integer specifying the total number iterations at which
               QTRAP will terminate even if the specified accuracy has not yet
               been met.    The maximum number of function evaluations will
               be 2^(MAX_ITER).   Default value is MAX_ITER = 20
       Any other keywords are passed directly to the user-supplied function
       via the _EXTRA facility.

       QTRAP is robust way of doing integrals that are not very smooth.  If the
       function has a continuous 3rd derivative then the function QSIMP will
          likely be more efficient at performing the integral.

       Compute the integral of sin(x) from 0 to !PI/3.
       IDL> QTRAP, 'sin', 0, !PI/3, S   & print,S
       The value obtained should be cos(!PI/3) = 0.5

       TRAPZD, ZPARCHECK

       W. Landsman         ST Systems Co.         August, 1991
       Continue after Max Iter warning message, W. Landsman  March 1996
       Converted to IDL V5.0   W. Landsman   September 1997
       Pass keyword to function via _EXTRA facility  W. Landsman July 1999

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