Your error is that you do not let the library load first you can do the following when the sun is loaded make a change of classes to execute the animation
$(function() {
$('button').addClass('animated rotateInDownLeft');
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/3.5.2/animate.min.css">
<button> myAnimatedButton </button>
Update
without jQuery you can use the following code:
//obteniendo el elemento que deseas animar
var elemento = document.getElementsByTagName("button")
//agregando el atributo class y sus valores
elemento[0].setAttribute("class","animated rotateInDownLeft")
//obteniendo el elemento que deseas animar
var elemento = document.getElementsByTagName("button")
//agregando el atributo class y sus valores
elemento[0].setAttribute("class","animated rotateInDownLeft")
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/3.5.2/animate.min.css">
<button> myAnimatedButton </button>