Industry Segment Information (Schedule of Revenue by Geographical Areas) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 770,743	$ 567,646	$ 474,692
Geographic Concentration [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 770,743	$ 567,646	$ 474,692
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	$ 94,472	$ 91,997	$ 79,581
Geographic Concentration [Member] | United States [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 394,080	$ 307,313	$ 259,557
Percentage	51.00%	54.00%	55.00%
Geographic Concentration [Member] | United States [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	75.00%	74.00%	81.00%
Long-lived tangible assets	$ 70,643	$ 68,526	$ 64,857
Geographic Concentration [Member] | International [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 376,663	$ 260,333	$ 215,135
Percentage	49.00%	46.00%	45.00%
Geographic Concentration [Member] | International [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	25.00%	26.00%	19.00%
Long-lived tangible assets	$ 23,829	$ 23,471	$ 14,724