If I check Wikipedia there's written, "Request may refer to: a question, a request for information or a petition, a formal document demanding something that is submitted to an authority"

Now when we are saying,"You should request a higher rate for the days you've worked last weekend" it means a kind of petition or something which I deserve, like I deserve to get a higher rate.

And, "You should request for a higher rate for the days you've worked last weekend" may mean sympathetically a bit, that it would've been helpful to get a higher rate.

However, both are correct to me.

If I check Wikipedia there's written,

Request may refer to:
a question, a request for information
or a petition, a formal document demanding something that is submitted to an authority

Now when we are saying,"You should request a higher rate for the days you've worked last weekend" it means a kind of petition or something which I deserve, like I deserve to get a higher rate.

And, "You should request for a higher rate for the days you've worked last weekend" may mean sympathetically a bit, that it would've been helpful to get a higher rate.

However, both are correct to me.