```/* nag_quad_2d_fin (d01dac) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 23, 2011.
*/

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd01.h>
#include <nagx01.h>

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL phi1(double y, Nag_Comm *comm);
static double NAG_CALL phi2a(double y, Nag_Comm *comm);
static double NAG_CALL fa(double x, double y, Nag_Comm *comm);
static double NAG_CALL phi2b(double y, Nag_Comm *comm);
static double NAG_CALL fb(double x, double y, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

int main(void)
{
static double ruser = {-1.0, -1.0, -1.0, -1.0, -1.0};
Integer  exit_status = 0;
Integer  npts, i;
double   absacc, ans, ya, yb;
Nag_Comm comm;
NagError fail;

INIT_FAIL(fail);

/* For communication with user-supplied functions: */
comm.user = ruser;

/* Skip heading in data file */
scanf("%*[^\n] ");
/* Input arguments */
scanf("%lf %lf", &ya, &yb);
scanf("%lf", &absacc);

for (i = 1; i <= 2; i++)
{
* Two-dimensional quadrature over a finite region.
*/
switch (i)
{
case 1:
printf("\nFirst formulation\n");
nag_quad_2d_fin(ya, yb, phi1, phi2a, fa, absacc, &ans, &npts,
&comm, &fail);
break;
case 2:
printf("\nSecond formulation\n");
nag_quad_2d_fin(ya, yb, phi1, phi2b, fb, absacc, &ans, &npts,
&comm, &fail);
break;
}
if (fail.code != NE_NOERROR)
{
fail.message);
exit_status = 1;
goto END;
}

printf("Integral = %9.4f\n"
"Number of function evaluations = %5ld\n", ans, npts);
}

END:
return exit_status;
}

static double NAG_CALL phi1(double y, Nag_Comm *comm)
{
if (comm->user == -1.0)
{
printf("(User-supplied callback phi1, first invocation.)\n");
comm->user = 0.0;
}
return 0.0;
}
static double NAG_CALL phi2a(double y, Nag_Comm *comm)
{
if (comm->user == -1.0)
{
printf("(User-supplied callback phi2a, first invocation.)\n");
comm->user = 0.0;
}
return (sqrt(1.0 - pow(y, 2)));
}
static double NAG_CALL fa(double x, double y, Nag_Comm *comm)
{
if (comm->user == -1.0)
{
printf("(User-supplied callback fa, first invocation.)\n");
comm->user = 0.0;
}
return (x + y);
}
static double NAG_CALL phi2b(double y, Nag_Comm *comm)
{
if (comm->user == -1.0)
{
printf("(User-supplied callback phi2b, first invocation.)\n");
comm->user = 0.0;
}
return (0.5 * nag_pi);
}
static double NAG_CALL fb(double x, double y, Nag_Comm *comm)
{
if (comm->user == -1.0)
{
printf("(User-supplied callback fb, first invocation.)\n");
comm->user = 0.0;
}
return (pow(y, 2) * (cos(x) + sin(x)));
}
```