#Code by Joseph Koutsoutis
Encode113 := proc(x) local a,b,c,d,eq1,eq2,eq3,eq4,i,S:
 eq1 := 0 = add(x[i], i=1..6) + a + b + c + d:
 eq2 := 0 = add(i * x[i], i=1..6) + 7*a + 8*b + 9*c + 10*d:
 eq3 := 0 = add(i^2 * x[i], i=1..6) + 7^2*a + 8^2*b + 9^2*c + 10^2*d:
 eq4 := 0 = add(i^3 * x[i], i=1..6) + 7^3*a + 8^3*b + 9^3*c + 10^3*d:
 S := msolve({eq1,eq2,eq3,eq4}, 11):
 subs(S, [op(x), a,b,c,d]):
end: 
#End Code by Joseph Koutsoutis