I think instance is a decent fix but it is necessary because of the mixing of Apache::Request and CGI. Any interesting test would be to swap the these two lines:

my $page = new CGI;
my $test=$apr->param('school');
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If you put the $apr->param request before CGI, then it should work (since CGI would not have had the chance to consume the POST). But ideally, I wouldn't mix Apache::Request with CGI.