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When the Productivity Detail report is run, it does not show the correct Billable hours for the date range selected.

Web TimeSheet can track the productivity hours on a monthly, quarterly and yearly basis only. Hence, when the Productivity Detail report is run with a certain date range, which is less than a month, it will always show the billable hours for the whole month, considering the date range is less than a month.
If the date range covers around 45 days or less, the report will show data for the two months within which the selected date range is covered in the report.

This is the normal behavior of the application, and is working as designed.