Hello,
I have to find the internal of
E_field := conjugate((-.7147663039-.8729430992*I)*exp((9.123185068*I)*cos(phi))*cos(phi)+(0.3187576278e-1+0.3371906130e-1*I)*sin(phi)*exp((4.561592534*I)*(-1.*sin(phi)+cos(phi)))+(0.7062621752e-1+.1302618973*I)*cos(phi)*exp((2.000000000*10^(-11)*I)*(53.*cos(phi)+1.570796328*10^11))+(-0.3187599160e-1-0.3371906130e-1*I)*sin(phi)*exp((4.561592534*I)*(sin(phi)+cos(phi))))*sin(phi):

I try to solve by
evalf(simpson(E_field, phi = 0..2*Pi));

restart:
with(student):
with(linalg):
# system of linear equations
A := array(evalf([[2, -1, sqrt(2)], [3, 2, -3], [3, sqrt(2), -15/7]])):
B := array(evalf([5 + 7*sqrt(2), -24, -12 - 3*sqrt(2)])):
B := `<,>`(B):
print(A):
print(B):
N := 3:
t := 1*10^(-6):

for j from 1 to N do
for k from j to N do
S := 0:
for i from 1 to N do
S := S + A[i,j]*A[i,k]:
end do: # end of i
C[k] := S:
end do: # end of k
C := 0: