# Domains
var x1 >= -4, <= 5;
var x2 >= -4, <= 5;
var x3 >= -4, <= 5;
var x4 >= -4, <= 5;
var x5 >= -4, <= 5;
var x6 >= -4, <= 5;
var x7 >= -4, <= 5;
var x8 >= -4, <= 5;
var x9 >= -4, <= 5;
var x10 >= -4, <= 5;
var l0 >= -1.0e16, <= 1.0e16;
var l1 >= -1.0e16, <= 1.0e16;
var l2 >= -1.0e16, <= 1.0e16;
var l3 >= -1.0e16, <= 1.0e16;
var l4 >= -1.0e16, <= 1.0e16;
var l5 >= -1.0e16, <= 1.0e16;
var l6 >= -1.0e16, <= 1.0e16;
var l7 >= -1.0e16, <= 1.0e16;
var l8 >= -1.0e16, <= 1.0e16;
var l9 >= -1.0e16, <= 1.0e16;
var l10 >= -1.0e16, <= 1.0e16;
var u1 >= -1.0e16, <= 1.0e16;
var u2 >= -1.0e16, <= 1.0e16;
var u3 >= -1.0e16, <= 1.0e16;
var u4 >= -1.0e16, <= 1.0e16;
var u5 >= -1.0e16, <= 1.0e16;
var u6 >= -1.0e16, <= 1.0e16;
var u7 >= -1.0e16, <= 1.0e16;
var u8 >= -1.0e16, <= 1.0e16;
var u9 >= -1.0e16, <= 1.0e16;
var u10 >= -1.0e16, <= 1.0e16;
var u11 >= -1.0e16, <= 1.0e16;

# Constants
param h := 1/(10+1);
param t1 := 1 * h;
param t2 := 2 * h;
param t3 := 3 * h;
param t4 := 4 * h;
param t5 := 5 * h;
param t6 := 6 * h;
param t7 := 7 * h;
param t8 := 8 * h;
param t9 := 9 * h;
param t10 := 10 * h;

subject to
cons1 : l0 = 0;
cons2 : l1 = l0 + t1*(x1+t1+1)^3;
cons3 : l2 = l1 + t2*(x2+t2+1)^3;
cons4 : l3 = l2 + t3*(x3+t3+1)^3;
cons5 : l4 = l3 + t4*(x4+t4+1)^3;
cons6 : l5 = l4 + t5*(x5+t5+1)^3;
cons7 : l6 = l5 + t6*(x6+t6+1)^3;
cons8 : l7 = l6 + t7*(x7+t7+1)^3;
cons9 : l8 = l7 + t8*(x8+t8+1)^3;
cons10 : l9 = l8 + t9*(x9+t9+1)^3;
cons11 : l10 = l9 + t10*(x10+t10+1)^3;
cons12 : u11 = 0;
cons13 : u1 = u2 + (1-t1)*(x1+t1+1)^3;
cons14 : u2 = u3 + (1-t2)*(x2+t2+1)^3;
cons15 : u3 = u4 + (1-t3)*(x3+t3+1)^3;
cons16 : u4 = u5 + (1-t4)*(x4+t4+1)^3;
cons17 : u5 = u6 + (1-t5)*(x5+t5+1)^3;
cons18 : u6 = u7 + (1-t6)*(x6+t6+1)^3;
cons19 : u7 = u8 + (1-t7)*(x7+t7+1)^3;
cons20 : u8 = u9 + (1-t8)*(x8+t8+1)^3;
cons21 : u9 = u10 + (1-t9)*(x9+t9+1)^3;
cons22 : u10 = u11 + (1-t10)*(x10+t10+1)^3;
cons23 : 0 = x1+0.5*h*((1-t1)*l1 + t1*u2);
cons24 : 0 = x2+0.5*h*((1-t2)*l2 + t2*u3);
cons25 : 0 = x3+0.5*h*((1-t3)*l3 + t3*u4);
cons26 : 0 = x4+0.5*h*((1-t4)*l4 + t4*u5);
cons27 : 0 = x5+0.5*h*((1-t5)*l5 + t5*u6);
cons28 : 0 = x6+0.5*h*((1-t6)*l6 + t6*u7);
cons29 : 0 = x7+0.5*h*((1-t7)*l7 + t7*u8);
cons30 : 0 = x8+0.5*h*((1-t8)*l8 + t8*u9);
cons31 : 0 = x9+0.5*h*((1-t9)*l9 + t9*u10);
cons32 : 0 = x10+0.5*h*((1-t10)*l10 + t10*u11);

solve;
display l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9, u1, u10, u11, u2, u3, u4, u5, u6, u7, u8, u9, x1, x10, x2, x3, x4, x5, x6, x7, x8, x9;