Industry Segment Information (Schedule of Revenue by Geographical Areas) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2021	Aug. 31, 2020	Aug. 31, 2019
Revenues from External Customers and Long-Lived Assets [Line Items]
Total Revenues	$ 567,646	$ 474,692	$ 444,072
Geographic Concentration [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Total Revenues	$ 567,646	$ 474,692	$ 444,072
Percentage	100.00%	100.00%	100.00%
Geographic Concentration [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	100.00%	100.00%	100.00%
Long-lived tangible assets	$ 91,997	$ 79,581	$ 68,968
Geographic Concentration [Member] | United States [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Total Revenues	$ 307,313	$ 259,557	$ 257,719
Percentage	54.00%	55.00%	58.00%
Geographic Concentration [Member] | United States [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	74.00%	81.00%	76.00%
Long-lived tangible assets	$ 68,526	$ 64,857	$ 52,187
Geographic Concentration [Member] | International [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Total Revenues	$ 260,333	$ 215,135	$ 186,353
Percentage	46.00%	45.00%	42.00%
Geographic Concentration [Member] | International [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	26.00%	19.00%	24.00%
Long-lived tangible assets	$ 23,471	$ 14,724	$ 16,781