4838.sagews

%cython
cdef extern from "math.h":
    double sin(double)

cdef double f(double x) except *:
    return sin(x**2)
        
def integrate(a, b, N):
    cdef int i
    cdef double dx, s=0
    dx = (b-a)/N
    for i in  range(N):
        s += f(a+i*dx)
    return s * dx

integrate(0,10,1e6)

0.58367343190152399