/*
n: 8;
xs: [1/12,2/12,4/12,5/12,7/12,8/12,10/12,11/12];
n: 7;
xs: [1/12,2/12,4/12,5/12,8/12,10/12,11/12];
n: 6;
xs: [1/12,2/12,5/12,7/12,10/12,11/12];
*/
n: 3;
xs: [1/6,3/6,5/6];
ws: makelist(concat(w,i),i,1,n);
ps: makelist(x^i,i,0,n-1); /* polynomials */
fs: makelist(buildq([i:i,ps:ps],lambda([x],ps[i])),i,1,n);
integ01: lambda([f],integrate(f(x),x,0,1));
Is: maplist(integ01,fs); /* calculate the integrals */
eq: lambda([f],lreduce("+",maplist(f,xs)*ws));
eqs: maplist(eq,fs)-Is; /* build equations */
solve(eqs,ws); /* solve for the weights */