Try dropping these use statements:

use LWP::Simple;
use HTTP::Request;
use HTTP::Cookies;
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and add:

use LWP;
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so your script will look something like this:

#!/usr/bin/perl

use strict;
use LWP;
use LWP::UserAgent;

my $URI = 'https://www.domain.com/protected_realm';
my $user = 'foo';
my $pass = 'bar';

# define user agent
my $ua = LWP::UserAgent->new();
$ua->agent("USER/AGENT/IDENTIFICATION");

# make request
my $request = HTTP::Request->new(GET => $URI);

# authenticate
$request->authorization_basic($user, $pass);

# except response
my $response = $ua->request($request);

# get content of response
my $content = $response->content();

# do whatever you need to do with the content here
print $content;

exit;
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It would be wise to add error checking in there as well. :)

Also, check out the docs for LWP here: LWP

And the LWP::UserAgent docs for your cookie related needs: LWP::UserAgent