Ah, I see the problem, I think. The array keys are confusing. Each array element is passed to the function
in the order that they are specified in the array - as call_user_func_array() would work with any other function - rather than to a specific named argument. So you can't rearrange the arguments or leave out middle ones. I should re-write the example code to better explain that, I suppose.
Your array was calling a function like this, which doesn't match the function definition:
CODE
CBS_KayakoAPI::getSubmittedTicketsWithExtraRestrictions("user", "pass", "mytest@email.com", 100, 1, 1, "lastactivity", false);
You'd be better off using something like: (/*..*/ comments added to make it clear what each argument is doing)
CODE
$result = CBS_KayakoAPI::getSubmittedTicketsWithExtraRestrictions($username, $password, $email, /*numPerPage*/ 100, /*page*/ 1, /*sortBy*/ 'lastactivity', /*orderAsc*/ false, /*minStartDate*/ -2147483648, /*maxStartDate*/ 2147483647, /*minLastActivity*/ -2147483648, /*maxLastActivity*/ 2147483647, /*minDueDate*/ -2147483648, /*maxDueDate*/ 2147483647, /*specificDepartment*/ 0, /*specificStatus*/ 1, /*specificPriority*/ 0);