I think it's a simple concatenation problem, but I can't get it right.

In the tests below, 1, 2, 3, and 4 give the expected behavior.
However tests 5, 6, and 7 give me false positives.
I am interpreting the false positives as  defined is only looking to see whether a value exists, which it does. However, &Mysimple_mod::bogus does not exist. I'm aware of using not_ok, but for this question I'm not trying to test for non-existent subroutines, I want to accurately make sure it is there. Later on in my journey I plan to write tests that actually use the subroutines. You'll see a few of my failed attempts in the .t file below.

The results:

1..7
ok 1 - use Mysimple_mod;
ok 2 - \#2 external is defined
ok 3 - \#3 internal is defined
not ok 4 - \#4 bogus subroutine
#   Failed test '\#4 bogus subroutine'
#   in test_Mysimple_mod.t at line 11.
ok 5 - \#5 bogus subroutine
ok 6 - \#6 bogus subroutine

&Mysimple_mod::bogus
ok 7 - \#7 bogus subroutine
# Looks like you failed 1 test of 7.
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use strict;
use warnings;

use Test::More tests => 7;                      
my $val = '&Mysimple_mod';

BEGIN { use_ok('Mysimple_mod', qw (external) ) };
ok ( defined( &external ) ,           "#2 external is defined");
ok ( defined( &Mysimple_mod::internal ) , "#3 internal is defined");
ok ( defined( &Mysimple_mod::bogus ) ,        "#4 bogus subroutine");
ok ( defined( "${val}".'::bogus' ) ,        "#5 bogus subroutine");
ok ( defined( ${val}.'::bogus' ) ,        "#6 bogus subroutine");

my $catval = "${val}" .'::bogus'; 
print "\n$catval\n";
ok ( defined( $catval ) ,                     "#7 bogus subroutine");
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#!/usr/bin/perl 

package Mysimple_mod;
use strict;
use warnings;

require Exporter;
our @ISA=qw(Exporter);
our @EXPORT_OK = qw( external );

sub external {
    my $val = shift;
    my $return_val = internal($val); 
    return $return_val;
    }

sub internal {
    my $val = shift;
    my $calc = $val * 3;
    return $calc;
    }

1;
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