integrate_lib

module integrate
contains

subroutine left(a,b,n,s,f)
implicit none
real(8)::a,b,h,s,f,x
integer::i,n
    h=(b-a)/n
do i=0,(n-1)
    x=a+h*i
    s=s+f(x)
end do
s=s*h
end subroutine left

subroutine right(a,b,n,s,f)
implicit none
real(8)::a,b,h,s,f,x
integer::i,n
h=(b-a)/n
do i=1,n
    x=a+h*i
    s=s+f(x)
end do
s=s*h
end subroutine right

subroutine mid(a,b,n,s,f)
implicit none
real(8)::a,b,h,s,f,x
integer::i,n
h=(b-a)/n
do i=1,n
    x=a+h*(i-1/2)
    s=s+f(x)
end do
s=s*h
end subroutine mid

subroutine tr(a,b,n,s,f)
implicit none
real(8)::a,b,h,s,f,x
integer::i,n
h=(b-a)/n
s=(f(a)+f(b))/2
do i=1,(n-1)
    x=a+h*i
    s=s+f(x)
end do
s=s*h
end subroutine tr

subroutine sim(a,b,n,s,f)
implicit none
real(8)::a,b,h,s,s1,s2,f
integer::i,n
s1=0
s2=0
h=(b-a)/(2*n)
s=f(a)+f(b)
do i=1,(n-1)
    s1=s1+f(a+(2*i)*h)
end do
s1=s1*2
do i=1,n
    s2=s2+f(a+(2*i-1)*h)
end do
s2=s2*4
s=(s+s2+s1)*h/3
print*,s
end subroutine sim

end module integrate