Here is an example of an API call for the Learning Activity report filtered by content in a specific folder with enrollment dates starting on 05/12/2021
https://www.brainshark.com/brainshark/webservices_mobile/report.ashx?sid=23161106&sky=2022e6a14cd04ff2594ad83af0f13e8&uid=2752230&path=/Brainshark Reports/Enhanced Learning Reports/Learning Activity&category_id=4146923&customfilter=<filter><op n="AND"><op n="EQ"><field n="enrollment_status" dt="SelectList" dn="Course Completion Status"/><val>Completed</val></op></op></filter>&begin_date=2021-05-12
The Completion_Date column can be used in the Custom Filter but needs to be CompletionDate Example:
<filter><op n="EQ"><field n="CompletionDate" dt="Date" dn="CompletionDate" /><val>2023-06-12 10:00:00</val></op></filter>