in reply to WWW::Mechanize::Firefox question
$mech->click_button(name => 'Get anagrams');
is the thing that should work. You don't tell me how it fails for you, so I can't advise further on that front.
If WWW::Mechanize::Firefox tells you
I don't know which form to submit, sorry.
... that means that there is more than one form on the page. Use ->form_name or ->form_number to set the "current form", as documented in WWW::Mechanize::Firefox.
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Seekers of Perl Wisdom