+3,fast,\frac{4x^3}{5}
+4,medium-slow,\frac{6x^3}{5} - 15x^2 + 100x - 140
+5,slow-then-very-fast,"\begin{cases}
+\frac{ x^3 \left( 100 - x \right) }{50}, & \text{if } x \leq 50 \\
+\frac{ x^3 \left( 150 - x \right) }{100}, & \text{if } 50 < x \leq 68 \\
+\frac{ x^3 \left( 1274 + (x \bmod 3)^2 - 9 (x \bmod 3) - 20 \left\lfloor \frac{x}{3} \right\rfloor \right) }{1000}, & \text{if } 68 < x \leq 98 \\
+\frac{ x^3 \left( 160 - x \right) }{100}, & \text{if } x > 98 \\
+\end{cases}"
+6,fast-then-very-slow,"\begin{cases}
+\frac{ x^3 \left( 24 + \left\lfloor \frac{x+1}{3} \right\rfloor \right) }{50}, & \text{if } x \leq 15 \\
+\frac{ x^3 \left( 14 + x \right) }{50}, & \text{if } 15 < x \leq 35 \\
+\frac{ x^3 \left( 32 + \left\lfloor \frac{x}{2} \right\rfloor \right ) }{50}, & \text{if } x > 35 \\
+\end{cases}"