I can't use the monte_carlo_integral function, what am I doing wrong?
var('u,v')
r_uvN(u,v)=sqrt(abs(-(cos(u) + 2)*cos(v)^2*sin(u) - (cos(u) + 2)*sin(u)*sin(v)^2)^2 +
abs((cos(u) + 2)*cos(u)*cos(v))^2 + abs((cos(u) + 2)*cos(u)*sin(v))^2)
sS=integral(integral( r_uvN,(u,0,2*pi)),(v,0,2*pi) )
print('s symbolic : ',sS,' num : ',sS.n(20) )
f(u, v)= u * v
res=monte_carlo_integral(f, [0,0], [2,2], 10000) # abs tol 0.1
print(' with f :',res)
sNL=monte_carlo_integral(r_uvN, [0,2*pi], [0,2*pi], 10000)
print('with r_uvN numerical ?? : ',sNL)
