Add more examples from PAL paper

app.py

@@ -160,12 +160,28 @@ with block:
         )
     with gr.Accordion("Examples from Google PaLM/Minerva paper", open=False):
         gr.Examples(
-            examples=["A line parallel to y = 4x + 6 passes through (5, 10). What is the y-coordinate of the point where this line crosses the y-axis?"],
+            examples=[
+                "If y = 8 − 5x + 4x^2, what is the value of y when x = −2",
+                "If √400 = √81 + √n, then what is the value of n?",
+                "At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her fifth practice she made 48 free throws. How many free throws did she make at the first practice?",
+                "Which of the following points is farthest from the origin: (1, 4), (3, 5), (−6, 0), (−4, −2)?",
+                "John is 31 years younger than his dad. The sum of their ages is 53 years. How many years old is John’s dad?",
+                "Lines y = (3a + 2)x − 2 and 2y = (a − 4)x + 2 are parallel. What is the value of a?",
+                "What is the value of 3√(4^5 + 4^5 + 4^5 + 4^5)?"
+                "A line parallel to y = 4x + 6 passes through (5, 10). What is the y-coordinate of the point where this line crosses the y-axis?",
+                "Assume that the variance of the first n natural numbers is 10, and the variance of the first m even natural numbers is 16. Compute m + n.",
+                "For every a, b, b != a prove that (a^2 + b^2) / 2 > ((a + b) / 2)^2",
+                "A uniform solid disk starts from rest and rolls down an inclined plane without slipping. After some time, what fraction of the disk’s total kinetic energy is rotational kinetic energy? What of the following is the right choice? Explain your answer. (A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3",
+            ],
             inputs=request
         )
     with gr.Accordion("Miscellaneous examples", open=False):
         gr.Examples(
-            examples=["42 times 81", "What is the sum of the first 21 Fibonacci numbers?"],
+            examples=[
+                "What is the sum of the first 10 prime numbers?",
+                "42 times 81",
+                "What is the sum of the first 21 Fibonacci numbers?"
+            ],
             inputs=request
         )