I had this problem too, and it looks like everything has changed with the Google API.
Using sample code in docs I tried to do
$calendar = new Calendar();
This generated an error for the Calendar class not found. It turns out that everything was renamed, and I had to do the following:
$calendar = new Google_Service_Calendar_Calendar();
It looks like a naming convention to avoid conflicts, but it would be nice to update the documents. Therefore, to solve the OP problem today, he now solves his problem using:
$event = new Google_Service_Calendar_Event();
You can view the Google / Service / Calendar.php file and you should see all the relevant classes with this naming convention.
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