fourd_int.c integrate to find 5D volume under 4D surface 
Numerical quadrature, x=1 to x=3, y=0.5 to y=2, 
 z=0.25 to z=2.25, t=0.5 to t=2.5 

Using trapezoidal method 
f1(x,y,z,t)=x+2*y+3*z+4*t+5 
np=4,  hx=0.666667, hy=0.5, hz=0.666667, ht=0.666667 
256 function evaluations 
computed volume=775.704, exact volume=231, error=544.704 
f1(x,y,z,t)=x+2*y+3*z+4*t+5 
np=16,  hx=0.133333, hy=0.1, hz=0.133333, ht=0.133333 
65536 function evaluations 
computed volume=250.05, exact volume=231, error=19.0504 
f1(x,y,z,t)=x+2*y+3*z+4*t+5 
np=64,  hx=0.031746, hy=0.0238095, hz=0.031746, ht=0.031746 
16777216 function evaluations 
computed volume=232.055, exact volume=231, error=1.05508 

f2(x,y,z,t)=x*x+2*y*y+3*z*z+4*t*t+5*x*y+6*x*z+7*y*z+ 
            8*x*t+9*y*t+10*z*t+ 
            11*x+12*y+23*z+14*t+15 
np=4,  hx=0.666667, hy=0.5, hz=0.666667, ht=0.666667 
256 function evaluations 
computed volume=9123.49, exact volume=2684, error=6439.49 
f2(x,y,z,t)=x*x+2*y*y+3*z*z+4*t*t+5*x*y+6*x*z+7*y*z+ 
            8*x*t+9*y*t+10*z*t+ 
            11*x+12*y+23*z+14*t+15 
np=16,  hx=0.133333, hy=0.1, hz=0.133333, ht=0.133333 
65536 function evaluations 
computed volume=2908.74, exact volume=2684, error=224.742 
f2(x,y,z,t)=x*x+2*y*y+3*z*z+4*t*t+5*x*y+6*x*z+7*y*z+ 
            8*x*t+9*y*t+10*z*t+ 
            11*x+12*y+23*z+14*t+15 
np=64,  hx=0.031746, hy=0.0238095, hz=0.031746, ht=0.031746 
16777216 function evaluations 
computed volume=2696.44, exact volume=2684, error=12.4448 

f3(x,y,z,t)=x*x*x+2*y*y*y+3*z*z*z+4*t*t*t+5*x*x*y+ 
            6*x*x*z+7*x*y*y+8*x*y*z+9*x*z*z+ 
            10*y*y*z+11*y*z*z+12*x*x*t+13*x*t*t+14*x*y*t+ 
            15*y*y*t+16*y*t*t+17*y*z*t+18*z*z*t+19*z*t*t+ 
            20*x*z*t+21*x*x+22*y*y+23*z*z+24*x*y+25*x*z+ 
            26*y*z+27*x*t+28*y*t+29*z*t+ 
            30*x+31*y+32*z+33*t+34 
np=4,  hx=0.666667, hy=0.5, hz=0.666667, ht=0.666667 
256 function evaluations 
computed volume=63801.3, exact volume=17976.2, error=45825 
f3(x,y,z,t)=x*x*x+2*y*y*y+3*z*z*z+4*t*t*t+5*x*x*y+ 
            6*x*x*z+7*x*y*y+8*x*y*z+9*x*z*z+ 
            10*y*y*z+11*y*z*z+12*x*x*t+13*x*t*t+14*x*y*t+ 
            15*y*y*t+16*y*t*t+17*y*z*t+18*z*z*t+19*z*t*t+ 
            20*x*z*t+21*x*x+22*y*y+23*z*z+24*x*y+25*x*z+ 
            26*y*z+27*x*t+28*y*t+29*z*t+ 
            30*x+31*y+32*z+33*t+34 
np=16,  hx=0.133333, hy=0.1, hz=0.133333, ht=0.133333 
65536 function evaluations 
computed volume=19564.3, exact volume=17976.2, error=1588.01 
f3(x,y,z,t)=x*x*x+2*y*y*y+3*z*z*z+4*t*t*t+5*x*x*y+ 
            6*x*x*z+7*x*y*y+8*x*y*z+9*x*z*z+ 
            10*y*y*z+11*y*z*z+12*x*x*t+13*x*t*t+14*x*y*t+ 
            15*y*y*t+16*y*t*t+17*y*z*t+18*z*z*t+19*z*t*t+ 
            20*x*z*t+21*x*x+22*y*y+23*z*z+24*x*y+25*x*z+ 
            26*y*z+27*x*t+28*y*t+29*z*t+ 
            30*x+31*y+32*z+33*t+34 
np=64,  hx=0.031746, hy=0.0238095, hz=0.031746, ht=0.031746 
16777216 function evaluations 
computed volume=18064.1, exact volume=17976.2, error=87.8797 

fe(x,y,z)=exp(x)*exp(y)*exp(z)*exp(t)    np=4 
np=4,  hx=0.666667, hy=0.5, hz=0.666667, ht=0.666667 
256 function evaluations 
computed volume=46813.2, exact volume=8615.15, error=38198.1 
fe(x,y,z)=exp(x)*exp(y)*exp(z)*exp(t)    np=16 
np=16,  hx=0.133333, hy=0.1, hz=0.133333, ht=0.133333 
65536 function evaluations 
computed volume=9837.14, exact volume=8615.15, error=1221.99 
fe(x,y,z)=exp(x)*exp(y)*exp(z)*exp(t)    np=64 
np=64,  hx=0.031746, hy=0.0238095, hz=0.031746, ht=0.031746 
16777216 function evaluations 
computed volume=8682.29, exact volume=8615.15, error=67.141 

Using Gauss Legendre method 
Gauss Legendre  np=4 
f1(x,y,z,t)=x+2*y+3*z+4*t+5; 
256 function evaluations 
computed volume=231, exact volume=231, error=-5.57066e-12 

Gauss Legendre  np=4 
f2(x,y,z,t)=x*x+2*y*y+3*z*z+4*t*t+5*x*y+6*x*z+7*y*z+ 
            8*x*t+9*y*t+10*z*t+ 
            11*x+12*y+23*z+14*t+15 
256 function evaluations 
computed volume=2684, exact volume=2684, error=-6.36646e-11 

Gauss Legendre  np=4 
f3(x,y,z,t)=x*x*x+2*y*y*y+3*z*z*z+4*t*t*t+5*x*x*y+ 
            6*x*x*z+7*x*y*y+8*x*y*z+9*x*z*z+ 
            10*y*y*z+11*y*z*z+12*x*x*t+13*x*t*t+14*x*y*t+ 
            15*y*y*t+16*y*t*t+17*y*z*t+18*z*z*t+19*z*t*t+ 
            20*x*z*t+21*x*x+22*y*y+23*z*z+24*x*y+25*x*z+ 
            26*y*z+27*x*t+28*y*t+29*z*t+ 
            30*x+31*y+32*z+33*t+34 
256 function evaluations 
computed volume=17976.2, exact volume=17976.2, error=-4.36557e-10 
Gauss Legendre  np=8 
f3(x,y,z,t)=x*x*x+2*y*y*y+3*z*z*z+4*t*t*t+5*x*x*y+ 
            6*x*x*z+7*x*y*y+8*x*y*z+9*x*z*z+ 
            10*y*y*z+11*y*z*z+12*x*x*t+13*x*t*t+14*x*y*t+ 
            15*y*y*t+16*y*t*t+17*y*z*t+18*z*z*t+19*z*t*t+ 
            20*x*z*t+21*x*x+22*y*y+23*z*z+24*x*y+25*x*z+ 
            26*y*z+27*x*t+28*y*t+29*z*t+ 
            30*x+31*y+32*z+33*t+34 
4096 function evaluations 
computed volume=17976.2, exact volume=17976.2, error=-3.92902e-10 


fe(x,y,z)=exp(x)*exp(y)*exp(z)*exp(t)    np=4 
256 function evaluations 
computed volume=8615.14, exact volume=8615.15, error=-0.00336015 
fe(x,y,z)=exp(x)*exp(y)*exp(z)*exp(t)    np=8 
4096 function evaluations 
computed volume=8615.15, exact volume=8615.15, error=3.27418e-11 
fe(x,y,z)=exp(x)*exp(y)*exp(z)*exp(t)    np=16 
65536 function evaluations 
computed volume=8615.15, exact volume=8615.15, error=-3.63798e-12