module fun_parameter
                integer t
                real x(7), f(7), fi(7)
        end module

        real function fun(x)
                real x
                fun = sin((x)**2)
!               print *, "in fun", fun
                return
        end


        real function lagrange (f_k)
                use fun_parameter
                real q
                real wkx(7), wkxk(7), f_k
                integer i, j
                q=0
                wkx(:)=1
                wkxk(:)=1
                do i=1,7
                       do j=1,7
                          if(i/=j) then
                            wkx(i)=wkx(i)*(f_k-x(j))
                            wkxk(i)=wkxk(i)*(x(i)-x(j))
                          endif
                       end do
                          if(wkxk(i)/=0) then
                                  q=q+((wkx(i)/wkxk(i))*f(i))
                          end if
                end do
                lagrange = q

        end

        real function lag_int(x)
                real x
                lag_int = x
                return
        end

        use fun_parameter
        external fun
        external lagrange
        integer            :: i, nofun
        integer, parameter :: N = 7, out=0
        real               :: points(n)
        REAL fun,A,B,ABSERR,RELERR,RES,ERREST,FLAG, lag_,summ
        A = 0
        B = 0.2d0
        F = 0
        X = 0
        RELERR = 1.e-06
        ABSERR = 0.0
        t = 0

        do i=1, 7
                X(i) = 0.2 * t
                F(i) = sin(X(i)**2)
                write(*,*) "x(", i, "),= ", x(i), "f(",i,") =", f(i)
                t = t+1
        end do

        call quanc8(fun,a,b,ABSERR,RELERR,RES,ERREST,nofun,FLAG)

        write(*,*) "integral f(x)=", res

        call quanc8(lagrange,a,b,ABSERR,RELERR,lag_,ERREST,nofun,FLAG)
        write(*,*) "untegral s(x)=", lag_


        stop
        end