Simple send an email via Mandrill API. I could not find this anywhere else so hopefully it is helpful to somebody else. At this point you should be able to look at the api docs and figure out the different options.

gistfile1.php

// Send Email

require_once 'Mandrill.php';
$mandrill = new Mandrill($apikey);

$message = new stdClass();
$message->html = "html message";
$message->text = "text body";
$message->subject = "email subject";
$message->from_email = "address@test.com";
$message->from_name  = "From Name";
$message->to = array(array("email" => "recipient@test.com"));
$message->track_opens = true;

$response = $mandrill->messages->send($message);