Here is an example for you to get you started.
My situation, our provider Ziggo ships crappy modems to their customers.
In order to prevent wifi drops etc i made this script to reboot it at night.
The router has a login page, i then have to navigate to advanced, then click reboot.
curl -s -L -c /var/tmp/modem_reboot_cookie.txt --referer http://$Modem_Adres/login_zig.asp -d "Zigloginnaam=$Modem_Gebruiker" "Zigpassword=$Modem_Wachtwoord" -d "login=Log+In" http://$Modem_Adres/goform/login_zig > /dev/null
curl -s --cookie /var/tmp/modem_reboot_cookie.txt --referer http://$Modem_Adres/Devicerestart.asp -d "mtenRestore=Device+Restart" -d "devicerestart=1" http://$Modem_Adres/goform/Devicerestart > /dev/null
Zigloginnaam and Zigpassword are the field ID’s of the login form and can be found in the source code (for google chrome simply add view-source:YOURURL to the address bar). Same goes for any other buttons you need to press.
It is hard for us to guide you as we have no access to your page. However, if you have tried everything and cant solve it, you can always PM and well see if we get this to work for you