A simple mysql->connect problem

[Jonathan Freese]

This perl script:
#!/bin/perl -w
#

use DBI;
print "DBI::VERSION: $DBI::VERSION\n";
use DBD::mysql;
print "DBD::mysql::VERSION: " . $DBD::mysql::VERSION . "\n";

$host="localhost";
$database="mysql";
$user="root";
$password="myrootpassword";

$db=mysql->connect($host, $database, $user, $password);

produces the following result:
DBI::VERSION: 1.40
DBD::mysql::VERSION: 2.9003
Can't locate object method "connect" via package "mysql" (perhaps you forgot to load "mysql"?) at ./tester.prl line 14.

What am I doing wrong?