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These problems are intended to demonstrate the level of difficulty and the typical techniques for each round in the competition. It does not contain any of the actual competition problems.

Round 1: two minutes per problem.

1. ∫₀¹ (x⁴ + x²) dx
2. ∫₀¹ 1 / (x⁴ + x²) dx
3. ∫ sin⁵(x) cos³(x) dx
4. ∫₀² |x² − 1| dx
5. ∫_−1² x² sign(x) dx

Round 2: four minutes per problem.

6. ∫₀² min(x, √(4 − x²)) dx
7. ∫ x² / (x² + 2x + 1) dx
8. ∫ x² e^x dx

Round 3: five minutes per problem.

9. ∫ sin(ln x) dx
10. ∫ e^x(x ln x + ln x + 1) dx
11. ∫₀¹ [ arctan(x²) + (Ï€/4) √(tan((Ï€/4)x)) ] dx