Take the PHP-REST demo client: https://github.com/moodlehq/sample-ws-clients/tree/master/PHP-REST (or another one)
For each test, you will need to change the code between /// PARAMETERs as specified
Test 1) - Specify 1 or more assignment ids for which the user has 'mod/assign:grade' capability
/// PARAMETERS
$assignmentids[] = 3; // user has 'mod/assign:grade' capability for this assignment
$assignmentids[] = 4; // user has 'mod/assign:grade' capability for this assignment
$params = array('assignmentids'=>$assignmentids);
/// PARAMETERS
The web service should return the submissions for the specified assignments
Test 2) - Specify the status of the submissions
/// PARAMETERS
$assignmentids[] = 3; // user has 'mod/assign:grade' capability for this assignment
$assignmentids[] = 4; // user has 'mod/assign:grade' capability for this assignment
$params = array('assignmentids'=>$assignmentids, 'status'=>'submitted');
/// PARAMETERS
The web services shoudld return all submissions for the specified assignments where the status is submitted
Test 3) - Specify a range of timemodified values
/// PARAMETERS
$assignmentids[] = 3; // user has 'mod/assign:grade' capability for this assignment
$assignmentids[] = 4; // user has 'mod/assign:grade' capability for this assignment
$params = array('assignmentids'=>$assignmentids, 'since'=>1331862337, 'before'=>1331862900);
/// PARAMETERS
The web services shoudld return all submissions for the specified assignments where the timemodified value is between the specified range
Test 4) - An assignment is specified for which the user does not have the mod/assign:grade capability
/// PARAMETERS
$assignmentids[] = 20; //user does not have 'mod/assign:grade' capability for this assignment
$params = array('assignmentids'=>$assignmentids);
/// PARAMETERS
The web service returns a warning message