https://my_domain.com

https://my_domain.com/

https://my_domain.com/some_page/

https://my_domain.com/some_page

location / {
    # This is what I have tried so far
    rewrite ^(.*)my_domain.com$ $1/ break;

    # Remove trailing double slashes.
    if ($request_uri ~ "^[^?]*?//") {
        rewrite "^" $scheme://$host$uri permanent;
    }

    # Remove trailing slashes.
    rewrite ^/(.*)/$ /$1 permanent;

    # Rewrite page/0 and page/1 from url.
    # rewrite ^/(.*)/page/[01]$ /$1 redirect;

    proxy_pass                      http://backend_web;
    proxy_set_header                Host $host;
    proxy_set_header                X-Real-IP $remote_addr;
}