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$mech->submit_form(   # invoke the submit_form() object method.
  $form_string => $d, # Anything to the left of a 
...
      # you created it with one key (the contents of $param_string)
      # and no associated value.  So you get an error message.
);

$mech->submit_form(
  $form_string, $d,
...
    split( /=>\s+|,\s+/, $param_string ) 
  }
);