Industry Segment Information (Schedule of Revenue by Geographical Areas) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 674,084	$ 770,743	$ 567,646
Geographic Concentration [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 674,084	$ 770,743	$ 567,646
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	$ 99,681	$ 94,472	$ 91,997
Geographic Concentration [Member] | United States [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 347,238	$ 394,080	$ 307,313
Percentage	52.00%	51.00%	54.00%
Geographic Concentration [Member] | United States [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	77.00%	75.00%	74.00%
Long-lived tangible assets	$ 76,428	$ 70,643	$ 68,526
Geographic Concentration [Member] | International [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 326,846	$ 376,663	$ 260,333
Percentage	48.00%	49.00%	46.00%
Geographic Concentration [Member] | International [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	23.00%	25.00%	26.00%
Long-lived tangible assets	$ 23,253	$ 23,829	$ 23,471