how can solve a numerical integral?

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I try to solve a numerical fourth order Integral. But it has taken a lot of time without any solution or even warning. Could you please help me to find it's problem. My code is

clc
clear all
close all
syms r R b r1 r2 r3 r4 r5 r6 z z1 z2 z3 z4 z5 z6
%syms r R b r1 r2 z z1 z2
hc=197.326;
alphas=1.54;
a=25.13;
l=-8/3;
s=1;
e=0.5;
M=313;
b=0.603;
f1=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*(r.^2+(s./2).^2-r.*s.*cos(z))));
f2=(1./pi.*b.^2)^(3./4).*(exp((-1./b.^2).*(r.^2+(s./2).^2+r.*s.*cos(z))));
k=(int(int(f1.*f2,'r',0,inf ),'z',0,pi));
N=(1+e.^2+2.*e.*k).^(1./2);
fl_1(r1)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r1).^2+(s./2).^2-(r1).*s.*cos(z1))));
fl_2(r2)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r2).^2+(s./2).^2-(r2).*s.*cos(z2))));
fl_3(r3)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r3).^2+(s./2).^2-(r3).*s.*cos(z3))));
fl_4(r4)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r4).^2+(s./2).^2-(r4).*s.*cos(z4))));
fl_5(r5)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r5).^2+(s./2).^2-(r5).*s.*cos(z5))));
fl_6(r6)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r6).^2+(s./2).^2-(r6).*s.*cos(z6))));
fR_1(r1)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r1).^2+(s./2).^2+(r1).*s.*cos(z1))));
fR_2(r2)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r2).^2+(s./2).^2+(r2).*s.*cos(z2))));
fR_3(r3)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r3).^2+(s./2).^2+(r3).*s.*cos(z3))));
fR_4(r4)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r4).^2+(s./2).^2+(r4).*s.*cos(z4))));
fR_5(r5)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r5).^2+(s./2).^2+(r5).*s.*cos(z5))));
fR_6(r6)=(1./pi.*b.^2).^(3./4).*(exp((-1./b.^2).*((r6).^2+(s./2).^2+(r6).*s.*cos(z6))));
uL_1(r1)=(fl_1(r1)+e.*fR_1(r1))./N;
uL_2(r2)=(fl_2(r2)+e.*fR_2(r2))./N;
uL_3(r3)=(fl_3(r3)+e.*fR_3(r3))./N;
uR_4(r4)=(fR_4(r4)+e.*fl_4(r4))./N;
uR_5(r5)=(fR_5(r5)+e.*fl_5(r5))./N;
uR_6(r6)=(fR_6(r6)+e.*fl_6(r6))./N;
g1=uL_1(r1).*uL_2(r2).*(1./(r1-r2)).*uL_1(r1).*uL_2(r2).*(r1).^2.*(r2).^2.*sin(z1).*sin(z2);
g2= matlabFunction(g1);
G_11= integral2(@(r1,r2)arrayfun(@(r1,r2)integral2(@(z1,z2)(g2(r1,r2,z1,z2)),0,pi,0,pi),r1,r2),1,2,@(r1)r1,2); 
G_12= integral2(@(r1,r2)arrayfun(@(r1,r2)integral2(@(z1,z2)(g2(r1,r2,z1,z2)),0,pi,0,pi),r1,r2),1,2,1,@(r1)r1);
G_1=G_11+G_12;
G_2=3.*(l./4).*(hc).*(alphas).*(2.*pi).^2.*(G_1);
g4=uR_4(r4).*uR_6(r6).*(1./(r4-r6)).*uR_4(r4).*uR_6(r6).*(r4).^2.*(r6).^2.*sin(z4).*sin(z6);
g6= matlabFunction(g4);
G_44= integral2(@(r4,r6)arrayfun(@(r4,r6)integral2(@(z4,z6)(g6(r4,r6,z4,z6)),0,pi,0,pi),r4,r6),1,2,@(r4)r4,2); 
G_46= integral2(@(r4,r6)arrayfun(@(r4,r6)integral2(@(z4,z6)(g6(r4,r6,z4,z6)),0,pi,0,pi),r4,r6),1,2,1,@(r4)r4);
G_4=G_44+G_46;
G_6=3.*(l./4).*(hc).*(alphas).*(2.*pi).^2.*(G_4);
g3=uL_3(r3).*uR_5(r5).*(1./(r3-r5)).*uL_3(r3).*uR_5(r5).*(r3).^2.*(r5).^2.*sin(z3).*sin(z5);
g5= matlabFunction(g3);
G_33= integral2(@(r3,r5)arrayfun(@(r3,r5)integral2(@(z3,z5)(g5(r3,r5,z3,z5)),0,pi,0,pi),r3,r5),1,2,@(r3)r3,2); 
G_35= integral2(@(r3,r5)arrayfun(@(r3,r5)integral2(@(z3,z5)(g5(r3,r5,z3,z5)),0,pi,0,pi),r3,r5),1,2,1,@(r3)r3);
G_3=G_33+G_35;
G_5=3.*(l./4).*(hc).*(alphas).*(2.*pi).^2.*(G_3);
V_g=G_2+G_6+G_5