$mech->post( $url, $field_name => $value,... Content => $content );
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Well I think you don't need Mech, just LWP::UserAgent.

Or, since WWW::Mechanize is a subclass of LWP::UserAgent, you could just use LWP::UserAgent's method post() on the mechanize object.
"What should it profit a man, if he should win a flame war, yet lose his cool?"

So is it as simple as something like this:

my $url = 'http://somewebsite?with_form_data';
$mech->post( $url );
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using my current $mech object?