question: The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).
  
  Pedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.
  
query_wo: Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
  Question: The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).
  
  Pedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.
  
query_cot: Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
  Question: The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).
  
  Pedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.
  
question_for_eval: The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).
  
  Pedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.
  