SUBROUTINE QK61(F,A,B,RESULT,ABSERR,RESABS,RESASC)
C***BEGIN PROLOGUE  QK61
C***DATE WRITTEN   800101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  H2A1A2
C***KEYWORDS  61-POINT GAUSS-KRONROD RULES
C***AUTHOR  PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. -
C             K. U. LEUVEN
C           DE DONCKER, ELISE, APPLIED MATH. AND PROGR. DIV. -
C             K. U. LEUVEN
C***PURPOSE  To compute I = Integral of F over (A,B) with error
C                           estimate
C                       J = Integral of DABS(F) over (A,B)
C***DESCRIPTION
C
C        Integration rule
C        Standard fortran subroutine
C        Real version
C
C
C        PARAMETERS
C         ON ENTRY
C           F      - Real
C                    Function subprogram defining the integrand
C                    function F(X). The actual name for F needs to be
C                    declared E X T E R N A L in the calling program.
C
C           A      - Real
C                    Lower limit of integration
C
C           B      - Real
C                    Upper limit of integration
C
C         ON RETURN
C           RESULT - Real
C                    Approximation to the integral I
C                    RESULT is computed by applying the 61-point
C                    Kronrod rule (RESK) obtained by optimal addition of
C                    abscissae to the 30-point Gauss rule (RESG).
C
C           ABSERR - Real
C                    Estimate of the modulus of the absolute error,
C                    which should equal or exceed DABS(I-RESULT)
C
C           RESABS - Real
C                    Approximation to the integral J
C
C           RESASC - Real
C                    Approximation to the integral of DABS(F-I/(B-A))
C***REFERENCES  (NONE)
C***ROUTINES CALLED  R1MACH
C***END PROLOGUE  QK61