I could not reproduce your error with your posted code. I got other compile errors which I fixed by adding/removing semicolons (see my "semi" comments). This code compiles and runs for me:

use warnings;
use strict;
use diagnostics;

my ($a, $b, $largest, $smallest);
print "Enter your First Number:\n";     # semi
chomp ($a = <>);
$largest = $a;
$smallest = $a;
print "Enter your Second Number:\n";    # semi
chomp ($b = <>);
if ($a > $b)                            # semi
{
        $largest=$a;
        $smallest=$b;
}
else
{
        $largest=$b;
        $smallest=$a;
}
print "The Biggest number is $largest and the smallest number is $smal
+lest\n";
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It is important to note that $a and $b are special variables to Perl.