eval can take either a block of code to trap runtime errors or a string to parse and sometimes execute at runtime. You're attempting to do the latter, but rather than pass a string as an argument you're passing a filehandle (<update>without the line delimiter implicitly undefined as in valdez's example</update>).

ehdonhon and sauoq's approaches are better if all you've got is Perl in those files, but this'll work too:

my $code;
open FILE, "/home/samn/cgi-bin/$page.rs" or die 'Monkeys!';
while (<FILE>) {
  $code .= $_;
}
eval $code;
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which places all the text in your file into a single string and eval's it.