Once you've done the

eval "require $class";
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part, you just need

$class->mysub();
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to call it. Here's a working example.

Module './pm_1175392/mymod123.pm':

package pm_1175392::mymod123;

sub mysub { return 'In package: ' . __PACKAGE__; }

1;
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Script './pm_1175392_variable_name_mod.pl':

#!/usr/bin/env perl -l

use strict;
use warnings;

my $modno = '123';
my $class = "pm_1175392::mymod$modno";
eval "require $class";

print $class->mysub();
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Sample run:

$ ./pm_1175392_variable_name_mod.pl
In package: pm_1175392::mymod123
$
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The require documentation has information on the eval part. See "perlobj: Invoking Class Methods" for information on the calling part.

Regarding the bit now "under the carpet", please don't do that. It's better to <strike> such text so that subsequent posts still make sense (all explained here). And, yes, I am "just across the ditch" :-)