mata
function integrate(f,a,b,n,u,v) {
	s = 0
	h = (b-a)/n
	m = length(u)
	for (i=0; i<n; i++) {
		x = a+i*h
		for (j=1; j<=m; j++) s = s+v[j]*(*f)(x+h*u[j])
	}
	return(s*h)
}

function log_(x) {
	return(log(x))
}

function id(x) {
	return(x)
}

function cube(x) {
	return(x*x*x)
}

function inv(x) {
	return(1/x)
}

function test(f,a,b,n) {
	return(integrate(f,a,b,n,(0,1),(1,0)),
	       integrate(f,a,b,n,(0,1),(0,1)),
	       integrate(f,a,b,n,(0.5),(1)),
	       integrate(f,a,b,n,(0,1),(0.5,0.5)),
	       integrate(f,a,b,n,(0,1/2,1),(1/6,4/6,1/6)))
}

test(&cube(),0,1,100)
test(&inv(),1,100,1000)
test(&id(),0,5000,5000000)
test(&id(),0,6000,6000000)
end