Business Combinations, Asset Acquisitions, and Joint Venture Formation (Details) $ in Thousands, € in Millions		3 Months Ended
	Sep. 04, 2024 USD ($)	Nov. 30, 2025 USD ($)	Nov. 30, 2024 USD ($)	Nov. 30, 2025 EUR (€)	Aug. 31, 2025 USD ($)	Sep. 04, 2024 EUR (€)
Business Combination [Line Items]
Payments to Acquire Businesses, Net of Cash Acquired		$ 0	$ 27,196
Goodwill		$ 287,988			$ 289,787
Developed Technology
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		7 years		7 years
Customer Relationships
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		14 years		14 years
Technology-Based Intangible Assets
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		7 years		7 years
DTA
Business Combination [Line Items]
Business Combination, Contingent Consideration, Liability | €				€ 2.5		€ 2.3
Payments to Acquire Businesses, Net of Cash Acquired	$ 26,700
Business Combination, Contingent Consideration, Range of Outcomes, Maximum, Amount | €						36.0
Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment		$ 2,841
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill		14,977
Business Combination, Recognized Asset Acquired, Asset, Current		6,299
Business Combination, Recognized Asset Acquired, Asset, Noncurrent		400
Business Combination, Recognized Liability Assumed, Liability, Current		(6,977)
Business Combination, Recognized Liability Assumed, Liability, Noncurrent		(5,563)
Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less)		26,661
Business Combination, Recognized Asset Acquired, Asset		39,201
Goodwill		$ 14,684
DTA | Maximum
Business Combination [Line Items]
Business Combination, Contingent Consideration, Liability | €						€ 12.0
DTA | Developed Technology
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		3 years		3 years
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived		$ 1,700
DTA | Customer Relationships
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		7 years		7 years
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived		$ 3,600
DTA | Technology-Based Intangible Assets
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		7 years		7 years
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived		$ 9,800