I'm not going to say that this is the best way to do it, just the first way that occurred to me. ;-)

#!/usr/bin/perl -w
use strict;

use Mail::CheckUser qw(:constants);

my @constants = @{ $Mail::CheckUser::EXPORT_TAGS{constants} };

foreach my $constant (@constants) {
  print $constant, " = ", eval($constant), $/;
}
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Updated: Now prints the names of all the constants and their values.

Added: outputs:

CU_OK = 0
CU_BAD_SYNTAX = 1
CU_UNKNOWN_DOMAIN = 2
CU_DNS_TIMEOUT = 3
CU_UNKNOWN_USER = 4
CU_SMTP_TIMEOUT = 5
CU_SMTP_UNREACHABLE = 6
[download]