Calculate Fees Due from Duration Range without Calendar Table Relationship

Here is what I would do. Use GENERATE to create a new calculated table. You can then link that table to your calendar table.

Table =    
SELECTCOLUMNS(            
	FILTER(                
		GENERATE( 
			'YourTable',
			'CalendarTable'
		),
		[Date] >= [from_date] &&
		[Date] < [billed_upto] 
	),
	"ID", [member_id],
	"Service", [service_name],
	"Amount",[amount],
	"Date", [Date]
) 

Something like that. At that point the problem should become trivial. Now the above assumes daily billing I suppose and you probably need monthly billing but that is the technique that I would use. You might just need a "calendar" table that was a list of months or month/years. If you could post some sample data in a format that can be copied and pasted easily, might be able to come up with a more specific solution.